Optimal Ternary Cubic Two-Weight Codes  

作　　者：SHI Minjia HUANG Daitao SOLE Patrick 

机构地区：[1]Key Laboratory of Intelligent Computing & Signal Processing, Ministry of Education, Anhui University, Hefei 230039, China [2]School of Mathematical Sciences, Anhui University, Hefei 230601, China [3]. CNRS//LAGA, University of Paris 8, 2 rue de la Libertg, 93 526 Saint-Denis, France

出　　处：《Chinese Journal of Electronics》2018年第4期734-738,共5页电子学报（英文版）

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)

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.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.

关 键 词：Three-weight codes Two-weight codes Gauss sums Trace codes 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]