Pub Date : 2024-05-06DOI: 10.13069/jacodesmath.v11i2.304
Maryam Bajelan, Mina Moeini, Bahattin Yildiz
In this paper, we investigate the Gray images of codes over chain rings, leading to the derivation of infinite families of self-orthogonal linear codes over the residue field $mathbb{F}_q$. We determine the parameters of optimal self-orthogonal and divisible linear codes. Additionally, we study the Gray images of quasi-twisted codes, resulting in some self-orthogonal Griesmer quasi-cyclic codes. Finally, we employ the CSS construction to derive some quantum codes based on self-orthogonal linear codes.
{"title":"Self-orthogonal and quantum codes over chain rings","authors":"Maryam Bajelan, Mina Moeini, Bahattin Yildiz","doi":"10.13069/jacodesmath.v11i2.304","DOIUrl":"https://doi.org/10.13069/jacodesmath.v11i2.304","url":null,"abstract":"In this paper, we investigate the Gray images of codes over chain rings, leading to the derivation of infinite families of self-orthogonal linear codes over the residue field $mathbb{F}_q$. We determine the parameters of optimal self-orthogonal and divisible linear codes. Additionally, we study the Gray images of quasi-twisted codes, resulting in some self-orthogonal Griesmer quasi-cyclic codes. Finally, we employ the CSS construction to derive some quantum codes based on self-orthogonal linear codes.","PeriodicalId":37029,"journal":{"name":"Journal of Algebra Combinatorics Discrete Structures and Applications","volume":" 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141129514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-05DOI: 10.13069/jacodesmath.1111720
D. Sarvate, Dinkayehu M. Woldemari̇am
{"title":"A note on $GDD(1, n, n , 4;lambda_{1},lambda_{2})$","authors":"D. Sarvate, Dinkayehu M. Woldemari̇am","doi":"10.13069/jacodesmath.1111720","DOIUrl":"https://doi.org/10.13069/jacodesmath.1111720","url":null,"abstract":"","PeriodicalId":37029,"journal":{"name":"Journal of Algebra Combinatorics Discrete Structures and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44343973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-05DOI: 10.13069/jacodesmath.1111746
Z. Balogh
: Let FG be the group algebra of a finite p -group G over a field F of characteristic p . Let (cid:126) be an involution of the group algebra FG which arises form the group basis G . The upper bound for the number of non-isomorphic (cid:126) -unitary subgroups is the number of conjugacy classes of the automorphism group G with all the elements of order two. The upper bound is not always reached in the case when G is an abelian group, but for non-abelian case the question is open. In this paper we present a non-abelian p -group G whose group algebra FG has sharply less number of non-isomorphic (cid:126) -unitary subgroups than the given upper bound.
{"title":"On the isomorphism of unitary subgroups of noncommutative group algebras","authors":"Z. Balogh","doi":"10.13069/jacodesmath.1111746","DOIUrl":"https://doi.org/10.13069/jacodesmath.1111746","url":null,"abstract":": Let FG be the group algebra of a finite p -group G over a field F of characteristic p . Let (cid:126) be an involution of the group algebra FG which arises form the group basis G . The upper bound for the number of non-isomorphic (cid:126) -unitary subgroups is the number of conjugacy classes of the automorphism group G with all the elements of order two. The upper bound is not always reached in the case when G is an abelian group, but for non-abelian case the question is open. In this paper we present a non-abelian p -group G whose group algebra FG has sharply less number of non-isomorphic (cid:126) -unitary subgroups than the given upper bound.","PeriodicalId":37029,"journal":{"name":"Journal of Algebra Combinatorics Discrete Structures and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44881644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-05DOI: 10.13069/jacodesmath.1111733
Christian Barrientos
{"title":"On the generation of alpha graphs","authors":"Christian Barrientos","doi":"10.13069/jacodesmath.1111733","DOIUrl":"https://doi.org/10.13069/jacodesmath.1111733","url":null,"abstract":"","PeriodicalId":37029,"journal":{"name":"Journal of Algebra Combinatorics Discrete Structures and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43056959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-05DOI: 10.13069/jacodesmath.1112177
E. Schwab
: Every gauge inverse submonoid (including Jones-Lawson’s gauge inverse submonoid of the polycyclic monoid P n ) is a normal submonoid. In 2018, Alyamani and Gilbert introduced an equivalence relation on an inverse semigroup associated to a normal inverse subsemigroup. The corresponding quotient set leads to an ordered groupoid. In this note we shall show that this ordered groupoid is inductive if the normal inverse subsemigroup is a gauge inverse submonoid and the corresponding quotient inverse semigroup by any guage inverse submonoid is isomorphic either to the bicyclic semigroup or to the bicyclic semigroup with adjoined zero.
{"title":"The bicyclic semigroup as the quotient inverse semigroup by any gauge inverse submonoid","authors":"E. Schwab","doi":"10.13069/jacodesmath.1112177","DOIUrl":"https://doi.org/10.13069/jacodesmath.1112177","url":null,"abstract":": Every gauge inverse submonoid (including Jones-Lawson’s gauge inverse submonoid of the polycyclic monoid P n ) is a normal submonoid. In 2018, Alyamani and Gilbert introduced an equivalence relation on an inverse semigroup associated to a normal inverse subsemigroup. The corresponding quotient set leads to an ordered groupoid. In this note we shall show that this ordered groupoid is inductive if the normal inverse subsemigroup is a gauge inverse submonoid and the corresponding quotient inverse semigroup by any guage inverse submonoid is isomorphic either to the bicyclic semigroup or to the bicyclic semigroup with adjoined zero.","PeriodicalId":37029,"journal":{"name":"Journal of Algebra Combinatorics Discrete Structures and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49031069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-15DOI: 10.13069/jacodesmath.1056485
Hirotaka Imamura, M. Kosuda, M. Oura
This is a continuation of our project which focuses on E-polynomials and the related combinatorics. A pair of groups appearing in the definition of E-polynomials yields the permutation group. In this paper, we determine the multi-matrix structures of the centralizer algebras of the tensor representations of this permutation group.
{"title":"Note on the permutation group associated to E-polynomials","authors":"Hirotaka Imamura, M. Kosuda, M. Oura","doi":"10.13069/jacodesmath.1056485","DOIUrl":"https://doi.org/10.13069/jacodesmath.1056485","url":null,"abstract":"This is a continuation of our project which focuses on E-polynomials and the related combinatorics. A pair of groups appearing in the definition of E-polynomials yields the permutation group. In this paper, we determine the multi-matrix structures of the centralizer algebras of the tensor representations of this permutation group.","PeriodicalId":37029,"journal":{"name":"Journal of Algebra Combinatorics Discrete Structures and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41403592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-15DOI: 10.13069/jacodesmath.1056555
F. J. González Vieli
{"title":"Growth of harmonic functions on biregular trees","authors":"F. J. González Vieli","doi":"10.13069/jacodesmath.1056555","DOIUrl":"https://doi.org/10.13069/jacodesmath.1056555","url":null,"abstract":"","PeriodicalId":37029,"journal":{"name":"Journal of Algebra Combinatorics Discrete Structures and Applications","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47577713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-15DOI: 10.13069/jacodesmath.1000842
S. Sharma, V. Sharma
{"title":"On metric dimension of plane graphs $mathfrak{J}_{n}$, $mathfrak{K}_{n}$ and $mathfrak{L}_{n}$","authors":"S. Sharma, V. Sharma","doi":"10.13069/jacodesmath.1000842","DOIUrl":"https://doi.org/10.13069/jacodesmath.1000842","url":null,"abstract":"","PeriodicalId":37029,"journal":{"name":"Journal of Algebra Combinatorics Discrete Structures and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41709515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-15DOI: 10.13069/jacodesmath.1000959
Karthick Gowthaman, Somi Gupta, Cruz Mohan, K. Guenda, Durairajan Chinnapillai
{"title":"Cyclic DNA codes over the ring $mathbb{Z}_4+umathbb{Z}_4+u^2mathbb{Z}_4$","authors":"Karthick Gowthaman, Somi Gupta, Cruz Mohan, K. Guenda, Durairajan Chinnapillai","doi":"10.13069/jacodesmath.1000959","DOIUrl":"https://doi.org/10.13069/jacodesmath.1000959","url":null,"abstract":"","PeriodicalId":37029,"journal":{"name":"Journal of Algebra Combinatorics Discrete Structures and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66233283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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