On the subfield subcodes of Hermitian codes

Fernando Pinero; Heeralal  Janwa

doi:10.1007/s10623-012-9736-9

On the subfield subcodes of Hermitian codes

Fernando Pinero, Heeralal Janwa

University of Puerto Rico

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

We present a fast algorithm using Gröbner basis to compute the dimensions of subfield subcodes of Hermitian codes. With these algorithms we are able to compute the exact values of the dimension of all subfield subcodes up to q ≤ 32 and length up to 215. We show that some of the subfield subcodes of Hermitian codes are at least as good as the previously known codes, and we show the existence of good long codes.

Original language	English
Journal	Designs, Codes and Cryptography
Volume	70
Issue number	1-2
Pages (from-to)	157-173
ISSN	0925-1022
DOIs	https://doi.org/10.1007/s10623-012-9736-9
Publication status	Published - 2014

Keywords

Subfield subcodes
Hermitian codes
Algebraic geometry codes
Gröbner basis
Decoding subfield subcodes
List-decoding of subfield subcodes

Access to Document

10.1007/s10623-012-9736-9

OpenUrl availability

Full text

Cite this

@article{b42a384c0925439cbefd3443104a8793,

title = "On the subfield subcodes of Hermitian codes",

abstract = "We present a fast algorithm using Gr{\"o}bner basis to compute the dimensions of subfield subcodes of Hermitian codes. With these algorithms we are able to compute the exact values of the dimension of all subfield subcodes up to q ≤ 32 and length up to 215. We show that some of the subfield subcodes of Hermitian codes are at least as good as the previously known codes, and we show the existence of good long codes.",

keywords = "Subfield subcodes, Hermitian codes, Algebraic geometry codes, Gr{\"o}bner basis, Decoding subfield subcodes, List-decoding of subfield subcodes",

author = "Fernando Pinero and Heeralal Janwa",

year = "2014",

doi = "10.1007/s10623-012-9736-9",

language = "English",

volume = "70",

pages = "157--173",

journal = "Designs, Codes and Cryptography",

issn = "0925-1022",

publisher = "Springer New York",

number = "1-2",

}

TY - JOUR

T1 - On the subfield subcodes of Hermitian codes

AU - Pinero, Fernando

AU - Janwa, Heeralal

PY - 2014

Y1 - 2014

N2 - We present a fast algorithm using Gröbner basis to compute the dimensions of subfield subcodes of Hermitian codes. With these algorithms we are able to compute the exact values of the dimension of all subfield subcodes up to q ≤ 32 and length up to 215. We show that some of the subfield subcodes of Hermitian codes are at least as good as the previously known codes, and we show the existence of good long codes.

AB - We present a fast algorithm using Gröbner basis to compute the dimensions of subfield subcodes of Hermitian codes. With these algorithms we are able to compute the exact values of the dimension of all subfield subcodes up to q ≤ 32 and length up to 215. We show that some of the subfield subcodes of Hermitian codes are at least as good as the previously known codes, and we show the existence of good long codes.

KW - Subfield subcodes

KW - Hermitian codes

KW - Algebraic geometry codes

KW - Gröbner basis

KW - Decoding subfield subcodes

KW - List-decoding of subfield subcodes

U2 - 10.1007/s10623-012-9736-9

DO - 10.1007/s10623-012-9736-9

M3 - Journal article

SN - 0925-1022

VL - 70

SP - 157

EP - 173

JO - Designs, Codes and Cryptography

JF - Designs, Codes and Cryptography

IS - 1-2

ER -

On the subfield subcodes of Hermitian codes

Abstract

Keywords

Access to Document

OpenUrl availability

Fingerprint

Cite this