The weight enumerators of several classes of p-ary cyclic codes

Abstract

a b s t r a c tLet p be an odd prime, and m and k be two positive integers with m ≥ 3. Let h ±1 (x) and h ±t (x) be the minimal polynomials of ±α −1 and ±α −t over F p , respectively, where α is a primitive element of F p m . Let C 1,−1,±t , C ±1,t,−t and C 1,−1,t,−t be the cyclic codes over F prespectively. This paper determines the weight distributions of the cyclic codes C 1,−1,±t , C ±1,t,−t and C 1,−1,t,−t for the parameter t satisfying some congruence equations.

Constant composition codes as subcodes of linear codes

“…Let p = 5, m = 3 and α is quare. By Magma, we have C D(α) is a [30, 3,20] code, whcih confirms the results in Table 1.…”

“…So, the corrosponing exponential sums can be computed by some technologies of finite field. Therefore, the weight distributions of a large number of linear codes (cyclic codes) were obtained (see [5,6,8,9,11,12,14,15,[17][18][19][20][21][22], and references theirin).…”

A Class of Linear Codes and Their Complete Weight Enumerators

“…In [3], [7], and [8], the authors studied the complete weight enumerators of some constant composition codes and presented some families of optimal constant composition codes. Weight distributions were also determined in [22], [28], [32], [34], [37], and [38] for different types of codes.…”

Complete weight enumerators of a class of linear codes with two or three weights

“…The weight enumerators of linear codes have been well studied in literature, such as [11,12,22,24,28,29] and references therein. The information of the complete weight enumerators of linear codes is of vital use because they can show the frequency of each symbol appearing in each codeword.…”