New Extremal Binary Self-Dual Codes from Block Circulant Matrices and Block Quadratic Residue Circulant Matrices
| Autor: | Alexander Tylyshchak, Abidin Kaya, Joe Gildea, Rhian Taylor, Bahattin Yildiz |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Discrete mathematics
Block (permutation group theory) Binary number 94B05 15B33 Mathematics - Rings and Algebras Construct (python library) Theoretical Computer Science Dual (category theory) Quadratic residue Combinatorics Rings and Algebras (math.RA) Code (cryptography) FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) Circulant matrix Mathematics |
| DOI: | 10.48550/arxiv.2003.05296 |
| Popis: | In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct self-dual codes of various lengths over F 2 and F 2 + u F 2 . Using extensions, neighbours and sequences of neighbours, we construct many new self-dual codes. In particular, we construct one new self-dual code of length 66 and 51 new self-dual codes of length 68. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|