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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.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.9 pp.1321-1328

- Publication Date
- 2021/09/01

- Publicized
- 2021/03/12

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2020EAP1119

- Type of Manuscript
- PAPER

- Category
- Coding Theory

Toru FUJIWARA

Osaka University

Takuya KUSAKA

Okayama University

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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Toru FUJIWARA, Takuya KUSAKA, "The Weight Distributions of the (256, k) Extended Binary Primitive BCH Codes with k≤71 and k≥187" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 9, pp. 1321-1328, September 2021, doi: 10.1587/transfun.2020EAP1119.

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.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020EAP1119/_p

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@ARTICLE{e104-a_9_1321,

author={Toru FUJIWARA, Takuya KUSAKA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={The Weight Distributions of the (256, k) Extended Binary Primitive BCH Codes with k≤71 and k≥187},

year={2021},

volume={E104-A},

number={9},

pages={1321-1328},

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.},

keywords={},

doi={10.1587/transfun.2020EAP1119},

ISSN={1745-1337},

month={September},}

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TY - JOUR

TI - The Weight Distributions of the (256, k) Extended Binary Primitive BCH Codes with k≤71 and k≥187

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1321

EP - 1328

AU - Toru FUJIWARA

AU - Takuya KUSAKA

PY - 2021

DO - 10.1587/transfun.2020EAP1119

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E104-A

IS - 9

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - September 2021

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.

ER -