☆ 4.3 Article

LCD and ACD codes over a noncommutative non-unital ring with four elements

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES (2022)

Self-orthogonal codes over a non-unital ring and combinatorial matrices

Minjia Shi et al.

Summary: This article studies a special construction of self-orthogonal codes, based on combinatorial matrices related to two-class association schemes, strongly regular graphs, and doubly regular tournaments. By constructing quasi self-dual codes and Type IV codes, the known bound on the minimum distance of Type IV codes over E is improved.

DESIGNS CODES AND CRYPTOGRAPHY (2023)

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Article Computer Science, Theory & Methods

Additive complementary dual codes over F4

Minjia Shi et al.

Summary: A linear code is considered a linear complementary dual (LCD) code if it meets its dual trivially. Due to its application in the security of embarked electronics, LCD codes have gained attention recently. Additive codes over F-4, which are stable under codeword addition but not necessarily under scalar multiplication, can be considered additive complementary dual (ACD) codes if they meet their dual trivially. This research aims to study codes that meet their dual trivially. The techniques and problems used in studying LCD codes are potentially relevant to ACD codes. Interesting constructions of ACD codes, using the trace Hermitian and trace Euclidean inner product, are given with respect to binary codes.

DESIGNS CODES AND CRYPTOGRAPHY (2023)

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Article Mathematics, Applied

DNA codes over two noncommutative rings of order four

Jon-Lark Kim et al.

Summary: This paper presents a new type of DNA codes over noncommutative rings E and F, based on quasi self-dual codes. By utilizing quasi self-duality, fixed GC-content constraint weight distributions and reverse-complement constraint minimum distributions of those codes can be described.

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING (2022)

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Article Mathematics, Applied

Type IV codes over a non-unital ring

Adel Alahmadi et al.

Summary: This paper studies the algebraic structure of linear codes over a special local ring E, including residue codes and torsion codes. The concepts of quasi self-dual codes and Type IV codes, which are quasi self-dual codes with all codewords having even Hamming weight, are introduced. The weight enumerators of these codes are analyzed using invariant theory and classified in short lengths.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS (2022)

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Proceedings Paper Computer Science, Theory & Methods