Pub Date : 2022-07-01DOI: 10.1134/S0032946022030048
V. I. Vorob'ev, V. Lebedev
{"title":"Improved Upper Bounds for the Rate of Separating and Completely Separating Codes","authors":"V. I. Vorob'ev, V. Lebedev","doi":"10.1134/S0032946022030048","DOIUrl":"https://doi.org/10.1134/S0032946022030048","url":null,"abstract":"","PeriodicalId":54581,"journal":{"name":"Problems of Information Transmission","volume":"58 1","pages":"242 - 253"},"PeriodicalIF":1.2,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47234542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-01DOI: 10.1134/S0032946022030085
E. A. Karatsuba
{"title":"Fast Evaluation Algorithms for Elementary Algebraic and Inverse Functions Using the FEE Method","authors":"E. A. Karatsuba","doi":"10.1134/S0032946022030085","DOIUrl":"https://doi.org/10.1134/S0032946022030085","url":null,"abstract":"","PeriodicalId":54581,"journal":{"name":"Problems of Information Transmission","volume":"2 6","pages":"284-296"},"PeriodicalIF":1.2,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41261451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-10DOI: 10.1134/s0032946022010057
A. S. Semenov, D. A. Shabanov
We study the threshold probability for the property of existence of a special-form (r)-coloring for a random (k)-uniform hypergraph in the (H(n,k,p)) binomial model. A parametric set of (j)-chromatic numbers of a random hypergraph is considered. A coloring of hypergraph vertices is said to be (j)-proper if every edge in it contains no more than (j) vertices of each color. We analyze the question of finding the sharp threshold probability of existence of a (j)-proper (r)-coloring for (H(n,k,p)). Using the second moment method, we obtain rather tight bounds for this probability provided that (k) and (j) are large as compared to (r).
{"title":"Bounds on Threshold Probabilities for Coloring Properties of Random Hypergraphs","authors":"A. S. Semenov, D. A. Shabanov","doi":"10.1134/s0032946022010057","DOIUrl":"https://doi.org/10.1134/s0032946022010057","url":null,"abstract":"<p>We study the threshold probability for the property of existence of a special-form <span>(r)</span>-coloring for a random <span>(k)</span>-uniform hypergraph in the <span>(H(n,k,p))</span> binomial model. A parametric set of <span>(j)</span>-chromatic numbers of a random hypergraph is considered. A coloring of hypergraph vertices is said to be <span>(j)</span>-proper if every edge in it contains no more than <span>(j)</span> vertices of each color. We analyze the question of finding the sharp threshold probability of existence of a <span>(j)</span>-proper <span>(r)</span>-coloring for <span>(H(n,k,p))</span>. Using the second moment method, we obtain rather tight bounds for this probability provided that <span>(k)</span> and <span>(j)</span> are large as compared to <span>(r)</span>.</p>","PeriodicalId":54581,"journal":{"name":"Problems of Information Transmission","volume":"12 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-10DOI: 10.1134/s0032946022010045
I. Yu. Mogilnykh
A code is said to be propelinear if its automorphism group contains a subgroup acting on its codewords regularly. A subgroup of the group (GA(r,q)) of affine transformations is said to be regular if it acts regularly on vectors of (mathbb{F}_q^r). Every automorphism of a regular subgroup of the general affine group (GA(r,q)) induces a permutation on the cosets of the Hamming code of length (frac{q^r-1}{q-1}). Based on this permutation, we propose a construction of (q)-ary propelinear perfect codes of length (frac{q^{r+1}-1}{q-1}). In particular, for any prime (q) we obtain an infinite series of almost full rank (q)-ary propelinear perfect codes.
{"title":"On q-ary Propelinear Perfect Codes Based on Regular Subgroups of the General Affine Group","authors":"I. Yu. Mogilnykh","doi":"10.1134/s0032946022010045","DOIUrl":"https://doi.org/10.1134/s0032946022010045","url":null,"abstract":"<p>A code is said to be propelinear if its automorphism group contains a subgroup acting on its codewords regularly. A subgroup of the group <span>(GA(r,q))</span> of affine transformations is said to be regular if it acts regularly on vectors of <span>(mathbb{F}_q^r)</span>. Every automorphism of a regular subgroup of the general affine group <span>(GA(r,q))</span> induces a permutation on the cosets of the Hamming code of length <span>(frac{q^r-1}{q-1})</span>. Based on this permutation, we propose a construction of <span>(q)</span>-ary propelinear perfect codes of length <span>(frac{q^{r+1}-1}{q-1})</span>. In particular, for any prime <span>(q)</span> we obtain an infinite series of almost full rank <span>(q)</span>-ary propelinear perfect codes.</p>","PeriodicalId":54581,"journal":{"name":"Problems of Information Transmission","volume":"8 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-01DOI: 10.1134/S0032946022020041
G. D. Dvorkin
{"title":"Geometric Interpretation of Entropy for Dyck Systems","authors":"G. D. Dvorkin","doi":"10.1134/S0032946022020041","DOIUrl":"https://doi.org/10.1134/S0032946022020041","url":null,"abstract":"","PeriodicalId":54581,"journal":{"name":"Problems of Information Transmission","volume":"58 1","pages":"137-143"},"PeriodicalIF":1.2,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42940055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-01DOI: 10.1134/S0032946022020077
V. Zyablov, F. Ivanov, E. Krouk, V. Sidorenko
{"title":"On New Problems in Asymmetric Cryptography Based on Error-Resistant Coding","authors":"V. Zyablov, F. Ivanov, E. Krouk, V. Sidorenko","doi":"10.1134/S0032946022020077","DOIUrl":"https://doi.org/10.1134/S0032946022020077","url":null,"abstract":"","PeriodicalId":54581,"journal":{"name":"Problems of Information Transmission","volume":"58 1","pages":"184 - 201"},"PeriodicalIF":1.2,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44845941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-01DOI: 10.1134/S0032946022020065
A. Kolnogorov
{"title":"Poissonian Two-Armed Bandit: A New Approach","authors":"A. Kolnogorov","doi":"10.1134/S0032946022020065","DOIUrl":"https://doi.org/10.1134/S0032946022020065","url":null,"abstract":"","PeriodicalId":54581,"journal":{"name":"Problems of Information Transmission","volume":"58 1","pages":"160-183"},"PeriodicalIF":1.2,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41912612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-01DOI: 10.1134/S003294602201001X
L. Bassalygo, V. Zinoviev, V. Lebedev
{"title":"Weakly Resolvable Block Designs and Nonbinary Codes Meeting the Johnson Bound","authors":"L. Bassalygo, V. Zinoviev, V. Lebedev","doi":"10.1134/S003294602201001X","DOIUrl":"https://doi.org/10.1134/S003294602201001X","url":null,"abstract":"","PeriodicalId":54581,"journal":{"name":"Problems of Information Transmission","volume":"58 1","pages":"1-12"},"PeriodicalIF":1.2,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64160762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-01DOI: 10.1134/S0032946022010033
S. Sharma, A. Sharma
{"title":"Multi-twisted Additive Codes with Complementary Duals over Finite Fields","authors":"S. Sharma, A. Sharma","doi":"10.1134/S0032946022010033","DOIUrl":"https://doi.org/10.1134/S0032946022010033","url":null,"abstract":"","PeriodicalId":54581,"journal":{"name":"Problems of Information Transmission","volume":"58 1","pages":"32-57"},"PeriodicalIF":1.2,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45526000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-01DOI: 10.1134/S0032946022010021
A. Barinov
{"title":"Reduction of Recursive Filters to Representations by Sparse Matrices","authors":"A. Barinov","doi":"10.1134/S0032946022010021","DOIUrl":"https://doi.org/10.1134/S0032946022010021","url":null,"abstract":"","PeriodicalId":54581,"journal":{"name":"Problems of Information Transmission","volume":"58 1","pages":"13-31"},"PeriodicalIF":1.2,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47161228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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