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Asymptotically good $ mathbb{Z}_{p}mathbb{Z}_{p}[u]/langle u^{t}rangle $-additive cyclic codes 渐近良$ mathbb{Z}_{p}mathbb{Z}_{p}[u]/langle u^{t}rangle $-可加循环码
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2023-01-01 DOI: 10.3934/amc.2022087
Ting Yao, Heqian Xu, Yongsheng Tang, Shixin Zhu
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引用次数: 0
Quasi-twisted codes as contractions of quasi-cyclic codes 拟旋码是拟循环码的压缩
4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2023-01-01 DOI: 10.3934/amc.2023041
Ferruh Özbudak, Buket Özkaya
We consider the quasi-twisted codes as contractions of quasi-cyclic codes and construct a family of $ q $-ary quasi-cyclic codes whose codewords have $ r $-divisible weights, where $ rmid q-1 $. We show that any quasi-cyclic code of co-index divisible by $ r $ is a direct sum of $ r $-divisible quasi-cyclic codes.
我们将拟扭曲码看作拟循环码的压缩,构造了一组$ q $一元的拟循环码,其码字具有$ r $-可整除的权值,其中$ r $中q $- 1 $。证明了任何可被r整除的拟循环码是r -可整除的拟循环码的直接和。
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引用次数: 0
Partial direct product difference sets and almost quaternary sequences 部分直积差分集与几乎四元序列
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2023-01-01 DOI: 10.3934/AMC.2021010
Büsra Özden, Oğuz Yayla
In this paper, we study the begin{document}$ m $end{document} -ary sequences with (non-consecutive) two zero-symbols and at most two distinct autocorrelation coefficients, which are known as almost begin{document}$ m $end{document} -ary nearly perfect sequences. We show that these sequences are equivalent to begin{document}$ ell $end{document} -partial direct product difference sets (PDPDS), then we extend known results on the sequences with two consecutive zero-symbols to non-consecutive case. Next, we study the notion of multipliers and orbit combination for begin{document}$ ell $end{document} -PDPDS. Finally, we present two construction methods for a family of almost quaternary sequences with at most two out-of-phase autocorrelation coefficients.
In this paper, we study the begin{document}$ m $end{document} -ary sequences with (non-consecutive) two zero-symbols and at most two distinct autocorrelation coefficients, which are known as almost begin{document}$ m $end{document} -ary nearly perfect sequences. We show that these sequences are equivalent to begin{document}$ ell $end{document} -partial direct product difference sets (PDPDS), then we extend known results on the sequences with two consecutive zero-symbols to non-consecutive case. Next, we study the notion of multipliers and orbit combination for begin{document}$ ell $end{document} -PDPDS. Finally, we present two construction methods for a family of almost quaternary sequences with at most two out-of-phase autocorrelation coefficients.
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引用次数: 0
Constructions of rotation symmetric Bent functions and Bent idempotent functions 旋转对称弯曲函数和弯曲幂等函数的构造
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2023-01-01 DOI: 10.3934/amc.2023022
Xiaoyan Chen, Sihong Su
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引用次数: 0
The number of codes over rings of order $ 4 $ containing a hull of given type 包含给定类型外壳的$ 4 $阶环上的代码数
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2023-01-01 DOI: 10.3934/amc.2023031
Steven T. Dougherty, Esengül Saltürk
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引用次数: 0
Some subfield codes from MDS codes MDS代码中的一些子字段代码
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2023-01-01 DOI: 10.3934/amc.2021023
Can Xiang, Jinquan Luo
Subfield codes of linear codes over finite fields have recently received a lot of attention, as some of these codes are optimal and have applications in secrete sharing, authentication codes and association schemes. In this paper, a class of binary subfield codes is constructed from a special family of MDS codes, and their parameters are explicitly determined. The parameters of their dual codes are also studied. Some of the codes presented in this paper are optimal or almost optimal.
有限域上线性码的子域码近年来受到了广泛的关注,因为其中一些子域码是最优的,在秘密共享、认证码和关联方案中有广泛的应用。本文利用一类特殊的MDS码构造了一类二进制子域码,并明确了它们的参数。研究了它们的双码参数。本文提出的一些编码是最优的或几乎最优的。
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引用次数: 1
A few more optimal optical orthogonal codes with non-constant auto-correlation function 几种具有非常数自相关功能的最优光学正交码
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2023-01-01 DOI: 10.3934/amc.2023029
Hengming Zhao, Rongcun Qin, M. Buratti, Dianhua Wu
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引用次数: 0
New bounds for covering codes of radius 3 and codimension $ 3t+1 $ 覆盖半径为3且余维为3t+1的码的新边界
4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2023-01-01 DOI: 10.3934/amc.2023042
Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco
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引用次数: 0
Several formulas for Bernoulli numbers and polynomials 伯努利数和多项式的几个公式
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2023-01-01 DOI: 10.3934/AMC.2021006
T. Komatsu, Bijan Kumar Patel, C. Pita-Ruiz
A generalized Stirling numbers of the second kind begin{document}$ S_{a,b}left(p,kright) $end{document} , involved in the expansion begin{document}$ left(an+bright)^{p} = sum_{k = 0}^{p}k!S_{a,b}left(p,kright) binom{n}{k} $end{document} , where begin{document}$ a neq 0, b $end{document} are complex numbers, have studied in [ 16 ]. In this paper, we show that Bernoulli polynomials begin{document}$ B_{p}(x) $end{document} can be written in terms of the numbers begin{document}$ S_{1,x}left(p,kright) $end{document} , and then use the known results for begin{document}$ S_{1,x}left(p,kright) $end{document} to obtain several new explicit formulas, recurrences and generalized recurrences for Bernoulli numbers and polynomials.
A generalized Stirling numbers of the second kind begin{document}$ S_{a,b}left(p,kright) $end{document} , involved in the expansion begin{document}$ left(an+bright)^{p} = sum_{k = 0}^{p}k!S_{a,b}left(p,kright) binom{n}{k} $end{document} , where begin{document}$ a neq 0, b $end{document} are complex numbers, have studied in [ 16 ]. In this paper, we show that Bernoulli polynomials begin{document}$ B_{p}(x) $end{document} can be written in terms of the numbers begin{document}$ S_{1,x}left(p,kright) $end{document} , and then use the known results for begin{document}$ S_{1,x}left(p,kright) $end{document} to obtain several new explicit formulas, recurrences and generalized recurrences for Bernoulli numbers and polynomials.
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引用次数: 1
Constructions of asymptotically optimal codebooks with respect to Welch bound and Levenshtein bound 关于Welch界和Levenshtein界的渐近最优码本构造
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2023-01-01 DOI: 10.3934/amc.2021065
Gang Wang, Deng-Ming Xu, Fang-Wei Fu
Codebooks with small maximum cross-correlation amplitudes are used to distinguish the signals from different users in code division multiple access communication systems. In this paper, several classes of codebooks are introduced, whose maximum cross-correlation amplitudes asymptotically achieve the corresponding Welch bound and Levenshtein bound. Specially, a class of optimal codebooks with respect to the Levenshtein bound is obtained. These classes of codebooks are constructed by selecting certain rows deterministically from circulant matrices, Fourier matrices and Hadamard matrices, respectively. The construction methods and parameters of some codebooks provided in this paper are new.
在码分多址通信系统中,利用最大互相关幅度较小的码本来区分来自不同用户的信号。本文介绍了几类码本,它们的最大互相关幅度渐近地达到相应的Welch界和Levenshtein界。特别地,得到了一类关于Levenshtein界的最优码本。这类码本分别通过从循环矩阵、傅里叶矩阵和Hadamard矩阵中确定性地选择某些行来构造。文中提供的一些码本的构造方法和参数是新的。
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引用次数: 0
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Advances in Mathematics of Communications
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