Standard

On explicit minimum weight bases for extended cyclic codes related to Gold functions. / Mogilnykh, I. Y.; Solov’eva, F. I.

In: Designs, Codes, and Cryptography, Vol. 86, No. 11, 01.11.2018, p. 2619-2627.

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

Harvard

Mogilnykh, IY & Solov’eva, FI 2018, 'On explicit minimum weight bases for extended cyclic codes related to Gold functions', Designs, Codes, and Cryptography, vol. 86, no. 11, pp. 2619-2627. https://doi.org/10.1007/s10623-018-0464-7

APA

Mogilnykh, I. Y., & Solov’eva, F. I. (2018). On explicit minimum weight bases for extended cyclic codes related to Gold functions. Designs, Codes, and Cryptography, 86(11), 2619-2627. https://doi.org/10.1007/s10623-018-0464-7

Vancouver

Mogilnykh IY, Solov’eva FI. On explicit minimum weight bases for extended cyclic codes related to Gold functions. Designs, Codes, and Cryptography. 2018 Nov 1;86(11):2619-2627. doi: 10.1007/s10623-018-0464-7

Author

Mogilnykh, I. Y. ; Solov’eva, F. I. / On explicit minimum weight bases for extended cyclic codes related to Gold functions. In: Designs, Codes, and Cryptography. 2018 ; Vol. 86, No. 11. pp. 2619-2627.

BibTeX

@article{3a5085bd3ff74d57ba8def9d7c352b25,
title = "On explicit minimum weight bases for extended cyclic codes related to Gold functions",
abstract = "Minimum weight bases of some extended cyclic codes can be chosen from the affine orbits of certain explicitly represented minimum weight codewords. We find such bases for the following three classes of codes: the extended primitive 2-error correcting BCH code of length n= 2 m, where m≥ 4 (for m≥ 20 the result was proven in Grigorescu and Kaufman IEEE Trans Inf Theory 58(I. 2):78–81, 2011), the extended cyclic code C¯ 1 , 5 of length n= 2 m, odd m, m≥ 5 , and the extended cyclic codes C¯1,2i+1 of lengths n= 2 m, (i,m)=1 and 3≤i≤m-54-o(m). ",
keywords = "Cyclic codes, Explicit basis, Gold function, Minimal weight basis",
author = "Mogilnykh, {I. Y.} and Solov{\textquoteright}eva, {F. I.}",
note = "Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",
year = "2018",
month = nov,
day = "1",
doi = "10.1007/s10623-018-0464-7",
language = "English",
volume = "86",
pages = "2619--2627",
journal = "Designs, Codes, and Cryptography",
issn = "0925-1022",
publisher = "Springer Netherlands",
number = "11",

}

RIS

TY - JOUR

T1 - On explicit minimum weight bases for extended cyclic codes related to Gold functions

AU - Mogilnykh, I. Y.

AU - Solov’eva, F. I.

N1 - Publisher Copyright: © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - Minimum weight bases of some extended cyclic codes can be chosen from the affine orbits of certain explicitly represented minimum weight codewords. We find such bases for the following three classes of codes: the extended primitive 2-error correcting BCH code of length n= 2 m, where m≥ 4 (for m≥ 20 the result was proven in Grigorescu and Kaufman IEEE Trans Inf Theory 58(I. 2):78–81, 2011), the extended cyclic code C¯ 1 , 5 of length n= 2 m, odd m, m≥ 5 , and the extended cyclic codes C¯1,2i+1 of lengths n= 2 m, (i,m)=1 and 3≤i≤m-54-o(m).

AB - Minimum weight bases of some extended cyclic codes can be chosen from the affine orbits of certain explicitly represented minimum weight codewords. We find such bases for the following three classes of codes: the extended primitive 2-error correcting BCH code of length n= 2 m, where m≥ 4 (for m≥ 20 the result was proven in Grigorescu and Kaufman IEEE Trans Inf Theory 58(I. 2):78–81, 2011), the extended cyclic code C¯ 1 , 5 of length n= 2 m, odd m, m≥ 5 , and the extended cyclic codes C¯1,2i+1 of lengths n= 2 m, (i,m)=1 and 3≤i≤m-54-o(m).

KW - Cyclic codes

KW - Explicit basis

KW - Gold function

KW - Minimal weight basis

UR - http://www.scopus.com/inward/record.url?scp=85042138333&partnerID=8YFLogxK

U2 - 10.1007/s10623-018-0464-7

DO - 10.1007/s10623-018-0464-7

M3 - Article

AN - SCOPUS:85042138333

VL - 86

SP - 2619

EP - 2627

JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

SN - 0925-1022

IS - 11

ER -

ID: 10421574