The weight distributions of the (256, k) extended binary primitive BCH codes with k ≤ 71 and k ≥ 187

Toru Fujiwara; Takuya Kusaka

doi:10.1587/transfun.2020EAP1119

The weight distributions of the (256, k) extended binary primitive BCH codes with k ≤ 71 and k ≥ 187

Research output: Contribution to journal › Article › peer-review

Abstract

Computing the weight distribution of a code is a challenging problem in coding theory. In this paper, the weight distributions of (256, k) extended binary primitive BCH codes with k ≤ 71 and k ≥ 187 are given. The weight distributions of the codes with k ≤ 63 and k ≥ 207 have already been obtained in our previous work. Affine permutation and trellis structure are used to reduce the computing time. Computer programs in C language which use recent CPU instructions, such as SIMD, are developed. These programs can be deployed even on an entry model workstation to obtain the new results in this paper.

Original language	English
Pages (from-to)	1321-1328
Number of pages	8
Journal	IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Volume	E104A
Issue number	9
DOIs	https://doi.org/10.1587/transfun.2020EAP1119
Publication status	Published - 2021

Keywords

Affine permutation
Automorphism group of code
BCH code
SIMD
Weight distribution

ASJC Scopus subject areas

Signal Processing
Computer Graphics and Computer-Aided Design
Electrical and Electronic Engineering
Applied Mathematics

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10.1587/transfun.2020EAP1119

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abstract = "Computing the weight distribution of a code is a challenging problem in coding theory. In this paper, the weight distributions of (256, k) extended binary primitive BCH codes with k ≤ 71 and k ≥ 187 are given. The weight distributions of the codes with k ≤ 63 and k ≥ 207 have already been obtained in our previous work. Affine permutation and trellis structure are used to reduce the computing time. Computer programs in C language which use recent CPU instructions, such as SIMD, are developed. These programs can be deployed even on an entry model workstation to obtain the new results in this paper.",

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T1 - The weight distributions of the (256, k) extended binary primitive BCH codes with k ≤ 71 and k ≥ 187

AU - Fujiwara, Toru

AU - Kusaka, Takuya

PY - 2021

Y1 - 2021

N2 - Computing the weight distribution of a code is a challenging problem in coding theory. In this paper, the weight distributions of (256, k) extended binary primitive BCH codes with k ≤ 71 and k ≥ 187 are given. The weight distributions of the codes with k ≤ 63 and k ≥ 207 have already been obtained in our previous work. Affine permutation and trellis structure are used to reduce the computing time. Computer programs in C language which use recent CPU instructions, such as SIMD, are developed. These programs can be deployed even on an entry model workstation to obtain the new results in this paper.

AB - Computing the weight distribution of a code is a challenging problem in coding theory. In this paper, the weight distributions of (256, k) extended binary primitive BCH codes with k ≤ 71 and k ≥ 187 are given. The weight distributions of the codes with k ≤ 63 and k ≥ 207 have already been obtained in our previous work. Affine permutation and trellis structure are used to reduce the computing time. Computer programs in C language which use recent CPU instructions, such as SIMD, are developed. These programs can be deployed even on an entry model workstation to obtain the new results in this paper.

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KW - Automorphism group of code

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The weight distributions of the (256, k) extended binary primitive BCH codes with k ≤ 71 and k ≥ 187

Abstract

Keywords

ASJC Scopus subject areas

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