The complete weight enumerator of the square of one-weight irreducible cyclic codes

被引:0
作者
Zhu, Canze [1 ]
机构
[1] Dongguan Univ Technol, Sch Comp Sci & Technol, Dongguan 523000, Peoples R China
关键词
Complete weight enumerators; Weight distributions; Squares of cyclic codes; Zeros of duals of cyclic codes; Symmetric matrices over F-q; HAMMING WEIGHTS; GAUSS SUMS; DISTRIBUTIONS; CONSTRUCTION; SEQUENCES; CURVES;
D O I
10.1007/s10623-025-01620-0
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
In this paper, for an odd prime power q and an integer m >= 2, let C(q,m) be a one-weight irreducible cyclic code with parameters [q(m)-1,m,(q-1)q(m-1)], we consider the complete weight enumerator and the weight distribution of the square (C(q,m))(2), whose dual has & LeftFloor;(m)/(2)& RightFloor;+1 zeros. Using the character sums method and the known result of counting mxm symmetric matrices over F-q with given rank, we explicitly determine the complete weight enumerator of (C(q,m))(2) and show that (C(q,m))(2) is a (2 & LeftFloor;(m)/(2)& RightFloor;+1)-weight cyclic code with parameters [q(m)-1,(m(m+1))/(2),(q-1)(q(m)-1-q(m-2))]. Moreover, we get the weight distribution of the square of the simplex code by puncturing the last (q-2)(q(m)-1)/(q-1) coordinates of (C(q,m))(2).
引用
收藏
页码:2779 / 2802
页数:24
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