SELF-DUALITY OF GENERALIZED TWISTED GABIDULIN CODES

Download

index.pdf

Date

2018-11-01

Author

Otal, KAMİL
Özbudak, Ferruh
Willems, Wofgang

Metadata

Show full item record

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

Item Usage Stats

191
views

73
downloads

Self-duality of Gabidulin codes was investigated in [10]and the authors provided an if and only if condition for a Gabidulin code to be equivalent to a self-dual maximum rank distance (MRD) code. In this paper, we investigate the analog problem for generalized twisted Gabidulin codes (a larger family of linear MRD codes including the family of Gabidulin codes). We observe that the condition presented in [10] still holds for generalized Gabidulin codes (an intermediate family between Gabidulin codes and generalized twisted Gabidulin codes). However, beyond the family of generalized Gabidulin codes we observe that some additional conditions are required depending on the additional parameters. Our tools are similar to those in [10] but we also use linearized polynomials, which leads to further tools and direct proofs.

Subject Keywords

Computer Networks and Communications, Algebra and Number Theory, Applied Mathematics, Discrete Mathematics and Combinatorics, Rank metric codes, Self-dual maximum rank distance codes, Generalized twisted Gabidulin codes, Linearized polynomials

URI

https://hdl.handle.net/11511/46603

Journal

ADVANCES IN MATHEMATICS OF COMMUNICATIONS

DOI

https://doi.org/10.3934/amc.2018042

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

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.
R-2 composition tests: a family of statistical randomness tests for a collection of binary sequences Uğuz, Muhiddin; Doğanaksoy, Ali (Springer Science and Business Media LLC, 2019-09-01) In this article a family of statistical randomness tests for binary strings are introduced, based on Golomb's pseudorandomness postulate R-2 on the number of runs. The basic idea is to construct recursive formulae with computationally tenable probability distribution functions. The technique is illustrated on testing strings of 2(7), 2(8), 2(10) and 2(12) bits. Furthermore, the expected value of the number of runs with a specific length is obtained. Finally the tests are applied to several collections of st...
Additive cyclic complementary dual codes over F4 Shi, Minjia; Liu, Na; Özbudak, Ferruh; Solé, Patrick (2022-10-01) © 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.
Results on symmetric S-boxes constructed by concatenation of RSSBs KAVUT, SELÇUK; Baloglu, Sevdenur (Springer Science and Business Media LLC, 2019-07-01) In this paper, we first present an efficient exhaustive search algorithm to enumerate 6 x 6 bijective S-boxes with the best-known nonlinearity 24 in a class of S-boxes that are symmetric under the permutation (x) = (x(0), x(2), x(3), x(4), x(5), x(1)), where x = (x(0), x1,...,x5)?26. Since any S-box S:?26?26 in this class has the property that S((x)) = (S(x)) for every x, it can be considered as a construction obtained by the concatenation of 5 x 5 rotation-symmetric S-boxes (RSSBs). The size of the search ...
A minimum distance bound for quasi-nD-cyclic codes Özbudak, Ferruh (Elsevier BV, 2016-09-01) We provide a new concatenated structure for multidimensional quasi-cyclic (QnDC) codes over F-q and we give a trace representation for their codewords, which extends the known representations of QC and nD cyclic codes. Based on these results, we obtain a minimum distance bound for QnDC dyclic codes. Since QnDC codes are naturally related to nD convolutional codes, this bound also applies to a special class of 1-generator 2D convolutional codes.

Citation Formats

K. Otal, F. Özbudak, and W. Willems, “SELF-DUALITY OF GENERALIZED TWISTED GABIDULIN CODES,” ADVANCES IN MATHEMATICS OF COMMUNICATIONS, pp. 707–721, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46603.