Optimal Ternary Cubic Two-Weight Codes
Optimal Ternary Cubic Two-Weight Codes作者机构：Key Laboratory of Intelligent Computing & Signal Processing Ministry of EducationAnhui University School of Mathematical Sciences Anhui University CNRS/LAGA University of Paris 8
出 版 物：《Chinese Journal of Electronics》 (电子学报(英文))
年 卷 期：2018年第27卷第4期
页 面：734-738页
核心收录：
学科分类：0839[工学-网络空间安全] 08[工学] 081201[工学-计算机系统结构] 0812[工学-计算机科学与技术（可授工学、理学学位）]
基 金：supported by National Natural Science Foundation of China(No.61672036) Excellent Youth Foundation of Natural Science Foundation of Anhui Province(No.1808085J20) Technology Foundation for Selected Overseas Chinese Scholar,Ministry of Personnel of China(No.05015133) Key projects of support program for outstanding young talents in Colleges and Universities(No.gxyqZD2016008)
主 题：Three-weight codes Two-weight codes Gauss sums Trace codes
摘 要：We study trace codes with defining set L,a subgroup of the multiplicative group of an extension of degree m of a certain ring of order 27. These codes are abelian, and their ternary images are quasi-cyclic of coindex three(a.k.a. cubic codes). Their Lee weight distributions are computed by using Gauss sums. These codes have three nonzero weights when m is singly-even. When m is odd, under some hypothesises on the size of L, we obtain two new infinite families of two-weight codes which are optimal. Applications of the image codes to secret sharing schemes are also given.
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