The complete weight distribution of a subclass of optimal three-weight cyclic codes

被引：4

作者：

Vega, Gerardo ^{[1
]}

Hernandez, Felix ^{[2
]}

机构：

[1] Univ Nacl Autonoma Mexico, Direcc Gen Comp & Tecnol Informac & Comunicac, Mexico City 04510, DF, Mexico

[2] Univ Nacl Autonoma Mexico, Posgrad Ciencia & Ingn Comp, Mexico City 04510, DF, Mexico

来源：

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2023年 / 15卷 / 02期

关键词：

Complete weight enumerator of a code; Weight distribution; Optimal three-weight cyclic codes; SUBFIELD SUBCODES; LINEAR CODES; ENUMERATORS;

D O I：

10.1007/s12095-022-00601-7

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The weight distribution of a code is usually investigated on the basis of Hamming weight, under which all the nonzero components of a codeword are regarded as identical. To describe the structure of nonbinary codes in more detail, each nonzero component should be distinguished from the other and this is done by means of the complete weight distribution. However, obtaining the complete weight distribution for nonbinary codes is an even harder problem than obtaining the ordinary weight distribution. Therefore, the complete weight distribution is unknown for most codes. The complete weight distributions of two classes of p-ary cyclic codes were recently reported by Heng and Yue (Cryptogr. Commun. 9, 323-343, 8). The purpose of this work is to present the complete weight distribution of a subclass of optimal three-weight cyclic codes over any finite field.

引用

页码：317 / 330

页数：14

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