On complementary dual multinegacirculant codes

Date

2020-01-01

Author

Alahmadi, Adel
Guneri, Cem
Özkaya, Buket
Shoaib, Hatoon
Sole, Patrick

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Linear codes with complementary duals intersect with their duals trivially. Multinegacirculant codes that are complementary dual are characterized algebraically and some good codes are found in this family. Exact enumeration is performed for indices 2 and 3, whereas special choices of the co-index and base field size are needed for higher indices. Asymptotic existence results are derived for the special class of such codes that have co-index a power of two by means of Dickson polynomials. This shows that there are infinite families of complementary dual multinegacirculant codes with relative distance satisfying a modified Gilbert-Varshamov bound.

Subject Keywords

LCD codes, Quasi-twisted codes, Gilbert-Varshamov bound

URI

https://hdl.handle.net/11511/103361

Journal

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES

DOI

https://doi.org/10.1007/s12095-019-00364-8

Collections

Graduate School of Applied Mathematics, Article

Citation Formats

A. Alahmadi, C. Guneri, B. Özkaya, H. Shoaib, and P. Sole, “On complementary dual multinegacirculant codes,” CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, vol. 12, no. 1, pp. 101–113, 2020, Accessed: 00, 2023. [Online]. Available: https://hdl.handle.net/11511/103361.