Cyclic Constant-Weight Codes: Upper Bounds and New Optimal Constructions

Liantao Lan; Yanxun Chang; Lidong Wang

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Cyclic Constant-Weight Codes: Upper Bounds and New Optimal Constructions

机译：循环恒重代码：上限和新的最佳构造

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In this paper, we consider optimal q-ary cyclic constant-weight codes of length n, minimum distance d, and weight w, briefly cyclic (n, d, w)q codes. We introduce the pure and mixed difference method to present a combinatorial description for a cyclic (n, d, w)q code and then obtain some tight upper bounds on the sizes of optimal cyclic (n, d, w)q codes. Finally, by using Skolem-type sequences, we completely determine the sizes of optimal cyclic (n, d, 3)3 codes with minimum distance 1 ≤ d ≤ 6.

机译：在本文中，我们考虑长度为n，最小距离为d，权重为w的最优q元循环恒权码，即短循环（n，d，w）q码。我们引入了纯差分和混合差分方法，以给出循环（n，d，w）q码的组合描述，然后在最佳循环（n，d，w）q码的大小上获得一些严格的上限。最后，通过使用Skolem型序列，我们可以完全确定最小距离1≤d≤6的最佳循环（n，d，3）3码的大小。

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来源
《Information Theory, IEEE Transactions on》 |2016年第11期|6328-6341|共14页
作者
Liantao Lan; Yanxun Chang; Lidong Wang;
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作者单位

Department of Mathematics, Beijing Jiaotong University, Beijing, China;

Department of Mathematics, Beijing Jiaotong University, Beijing, China;

Department of Basic Courses, Chinese People’s Armed Police Force Academy, Langfang, China;

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正文语种 eng
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关键词
Zinc; Orbits; Upper bound; Hamming distance; Electronic mail; Optical feedback; Additives;

机译：锌;轨道;上限;锤距;电子邮件;光反馈;添加剂;

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1. Constructions for optimal cyclic ternary constant-weight codes of weight four and distance six [J] . Lan Liantao, Chang Yanxun Discrete mathematics . 2018,第4期

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2. Constructions of binary constant-weight cyclic codes and cyclically permutable codes [J] . Nguyen Q. A, Gyorfi L. IEEE Transactions on Information Theory . 1992,第3期

机译：二进制恒权循环码和循环置换码的构造
3. Classification of Optimal (v, 4,1) Binary Cyclically Permutable Constant-Weight Codes and Cyclic 2-(v, 4,1) Designs with v < 76 [J] . T. Baicheva, S. Topalova Problems of information transmission . 2011,第3期

机译：最优（v，4,1）二元循环可置换恒定重量代码和v <76的循环2-（v，4,1）设计的分类
4. Constant-weight code bounds from spherical code bounds [C] . Agrell E., Vardy A., Zeger K. Information Theory, 2000. Proceedings. IEEE International Symposium on . -1

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5. Upper bounds on the performance of maximum-likelihood decoded binary block codes in AWGN and block fading channels. [D] . Mehrabian, Amaan. 2005

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6. Nonasymptotic Upper Bounds on Binary Single Deletion Codes via Mixed Integer Linear Programming [O] . Albert No 2019

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7. Constructions of binary constant-weight cyclic codes and cyclically permutable codes [O] . Nguyen Q. A, Z Gyiirfi, James L. Massey 1992

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Cyclic Constant-Weight Codes: Upper Bounds and New Optimal Constructions

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