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New extremal binary self-dual codes of length 68 from quadratic residue codes over F 2+uF2+u2F2

Authors:

Bahattin Yildiz,

Irfan SiapAuthors Info & Claims

Finite Fields and Their Applications, Volume 29

Pages 160 - 177

https://doi.org/10.1016/j.ffa.2014.04.009

Published: 01 September 2014 Publication History

Abstract

In this work, quadratic residue codes over the ring F"2+uF"2+u^2F"2 with u^3=u are considered. A duality and distance preserving Gray map from F"2+uF"2+u^2F"2 to F"2^3 is defined. By using quadratic double circulant, quadratic bordered double circulant constructions and their extensions self-dual codes of different lengths are obtained. As Gray images of these codes and their extensions, a substantial number of new extremal self-dual binary codes are found. More precisely, thirty two new extremal binary self-dual codes of length 68, 363 Type I codes of parameters [72,36,12], a Type II [72,36,12] code and a Type II [96,48,16] code with new weight enumerators are obtained through these constructions. The results are tabulated.

References

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Cited By

Gildea JKorban ARoberts A(2022)New binary self-dual codes of lengths 80, 84 and 96 from composite matricesDesigns, Codes and Cryptography10.1007/s10623-021-00976-390:2(317-342)Online publication date: 1-Feb-2022
https://dl.acm.org/doi/10.1007/s10623-021-00976-3
Dougherty SKorban AŞahinkaya SUstun D(2021)Group matrix ring codes and constructions of self-dual codesApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-021-00504-934:2(279-299)Online publication date: 2-Apr-2021
https://dl.acm.org/doi/10.1007/s00200-021-00504-9
Goyal MRaka M(2018)Quadratic residue codes over the ring źźp[u]/źumźuź$\mathbb {F}_{p}[u]/\langle u^{m}-u\rangle $ and their Gray imagesCryptography and Communications10.1007/s12095-017-0223-z10:2(343-355)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.1007/s12095-017-0223-z
Show More Cited By

New extremal binary self-dual codes of length 68 from quadratic residue codes over F 2+uF2+u2F2
1. Mathematics of computing
  1. Information theory
  2. Mathematical analysis
    1. Numerical analysis
2. Security and privacy
  1. Cryptography

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Published In

cover image Finite Fields and Their Applications

Finite Fields and Their Applications Volume 29, Issue

September, 2014

275 pages

ISSN:1071-5797

Issue’s Table of Contents

Copyright © Elsevier Inc. © 2014.

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 September 2014

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Cited By

Gildea JKorban ARoberts A(2022)New binary self-dual codes of lengths 80, 84 and 96 from composite matricesDesigns, Codes and Cryptography10.1007/s10623-021-00976-390:2(317-342)Online publication date: 1-Feb-2022
https://dl.acm.org/doi/10.1007/s10623-021-00976-3
Dougherty SKorban AŞahinkaya SUstun D(2021)Group matrix ring codes and constructions of self-dual codesApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-021-00504-934:2(279-299)Online publication date: 2-Apr-2021
https://dl.acm.org/doi/10.1007/s00200-021-00504-9
Goyal MRaka M(2018)Quadratic residue codes over the ring źźp[u]/źumźuź$\mathbb {F}_{p}[u]/\langle u^{m}-u\rangle $ and their Gray imagesCryptography and Communications10.1007/s12095-017-0223-z10:2(343-355)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.1007/s12095-017-0223-z
Raka MKathuria LGoyal M(2017)(1ź2u3)-constacyclic codes and quadratic residue codes over Fp[u]/źu4źuź$\mathbb {F}_{p}[u]/\langle u^{4}-u\rangle $Cryptography and Communications10.1007/s12095-016-0184-79:4(459-473)Online publication date: 1-Jul-2017
https://dl.acm.org/doi/10.1007/s12095-016-0184-7
Kaya AYildiz B(2016)Various constructions for self-dual codes over rings and new binary self-dual codesDiscrete Mathematics10.1016/j.disc.2015.09.010339:2(460-469)Online publication date: 6-Feb-2016
https://dl.acm.org/doi/10.1016/j.disc.2015.09.010
Yankov NMoon Ho Lee Gurel MIvanova M(2015)Self-Dual Codes With an Automorphism of Order 11IEEE Transactions on Information Theory10.1109/TIT.2015.239691561:3(1188-1193)Online publication date: 12-Feb-2015
https://dl.acm.org/doi/10.1109/TIT.2015.2396915
Kaya AYildiz BSiap I(2015)New extremal binary self-dual codes from F 4 + u F 4 -lifts of quadratic circulant codes over F 4Finite Fields and Their Applications10.1016/j.ffa.2015.05.00435:C(318-329)Online publication date: 1-Sep-2015
https://dl.acm.org/doi/10.1016/j.ffa.2015.05.004

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