Additive cyclic complementary dual codes over F4

Date

2022-10-01

Author

Shi, Minjia
Liu, Na
Özbudak, Ferruh
Solé, Patrick

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

241
views

0
downloads

© 2022 Elsevier Inc.An additive cyclic code of length n over F4 can be defined equivalently as an F2[x]/〈xn+1〉-submodule of F4[x]/〈xn+1〉. In this paper we study additive cyclic and complementary dual codes of odd length over F4 with respect to the trace Hermitian inner product and the trace Euclidean inner product. We characterize subfield subcodes and trace codes of these codes by their generators as binary cyclic codes.

Subject Keywords

Additive codes, Cyclic codes, Complementary dual, LCD CODES, Additive codes, Complementary dual, Cyclic codes

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85134430500&origin=inward
https://hdl.handle.net/11511/99175

Journal

Finite Fields and their Applications

DOI

https://doi.org/10.1016/j.ffa.2022.102087

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

A Bound on the Minimum Distance of Quasi-cyclic Codes Gueneri, Cem; Özbudak, Ferruh (2012-01-01) We give a general lower bound for the minimum distance of q-ary quasi-cyclic codes of length ml and index l, where m is relatively prime to q. The bound involves the minimum distances of constituent codes of length l as well as the minimum distances of certain cyclic codes of length m which are related to the fields over which the constituents are defined. We present examples which show that the bound is sharp in many instances. We also compare the performance of our bound against the bounds of Lally and Es...
Additive Rank Metric Codes Otal, KAMİL; Özbudak, Ferruh (2017-01-01) We give an infinite family of maximum rank distance (MRD) codes, which covers properly the largest known linear MRD code family. Our family contains infinite families of non-linear MRD codes, which are the first non-linear examples for most of the parameters. We also give explicit examples and a table that demonstrates the proportion of linear and non-linear families for some small parameters.
The Minimum Hamming Distance of Cyclic Codes of Length 2ps ÖZADAM, Hakan; Özbudak, Ferruh (2009-06-12) We study cyclic codes of length 2p(s) over F-q where p is an odd prime. Using the results of [1], we compute the minimum Hamming distance of these codes.
A NOTE ON NEGACYCLIC AND CYCLIC CODES OF LENGTH p(s) OVER A FINITE FIELD OF CHARACTERISTIC p ÖZADAM, Hakan; Özbudak, Ferruh (American Institute of Mathematical Sciences (AIMS), 2009-08-01) Recently, the minimum Hamming weights of negacyclic and cyclic codes of length p(s) over a finite field of characteristic p are determined in [4]. We show that the minimum Hamming weights of such codes can also be obtained immediately using the results of [1].
Multidimensional cyclic codes and Artin–Schreier type hypersurfaces over finite fields Güneri, Cem; Özbudak, Ferruh (Elsevier BV, 2008-1) We obtain a trace representation for multidimensional cyclic codes via Delsarte's theorem. This relates the weights of the codewords to the number of affine rational points of Artin-Schreier type hypersurfaces over finite fields. Using Deligne's and Hasse-Weil-Serre inequalities we get bounds on the minimum distance. Comparison of the bounds is made and illustrated by examples. Some applications of our results are given. We obtain a bound on certain character sums over F-2 which gives better estimates than ...

Citation Formats

M. Shi, N. Liu, F. Özbudak, and P. Solé, “Additive cyclic complementary dual codes over F4,” Finite Fields and their Applications, vol. 83, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85134430500&origin=inward.