A LINEAR CONSTRUCTION FOR CERTAIN KERDOCK AND PREPARATA CODES

被引：81

作者：

CALDERBANK, AR

HAMMONS, AR

KUMAR, PV

SLOANE, NJA

SOLE, P

机构：

[1] HUGHES AIRCRAFT CO,CANOGA PK,CA 91304

[2] UNIV SO CALIF,INST COMMUN SCI,LOS ANGELES,CA 90089

[3] CNRS,F-06560 VALBONNE,FRANCE

来源：

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 1993年 / 29卷 / 02期

关键词：

D O I：

10.1090/S0273-0979-1993-00426-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Nordstrom-Robinson, Kerdock, and (slightly modified) Preparata codes are shown to be linear over Z4, the integers mod 4. The Kerdock and Preparata codes are duals over Z4, and the Nordstrom-Robinson code is self-dual. All these codes are just extended cyclic codes over Z4. This provides a simple definition for these codes and explains why their Hamming weight distributions are dual to each other. First- and second-order Reed-Muller codes are also linear codes over Z4, but Hamming codes in general arc not, nor is the Golay code.

引用

页码：218 / 222

页数：5

共 26 条

[1] ON THE PREPARATA AND GOETHALS CODES [J].