\(2^n\) bordered constructions of self-dual codes from group rings
From MaRDI portal
Publication:1994917
DOI10.1016/j.ffa.2020.101692zbMath1464.94067OpenAlexW3047057787MaRDI QIDQ1994917
Abidin Kaya, Joe Gildea, Steven T. Dougherty
Publication date: 18 February 2021
Published in: Finite Fields and their Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.ffa.2020.101692
Linear codes (general theory) (94B05) Group rings (16S34) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Group rings of finite groups and their modules (group-theoretic aspects) (20C05)
Related Items
The weight enumerators of singly-even self-dual \([88,44,14\) codes and new binary self-dual \([68,34,12]\) and \([88,44,14]\) codes] ⋮ An improved upper bound on self-dual codes over finite fields \(\mathrm{GF}(11)\), \(\mathrm{GF}(19)\), and \(\mathrm{GF}(23)\) ⋮ New binary self-dual codes of lengths 80, 84 and 96 from composite matrices
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Codes over \(R_k\), Gray maps and their binary images
- Self-dual codes over commutative Frobenius rings
- Double circulant and quasi-twisted self-dual codes over \(\mathbb F_5\) and \(\mathbb F_7\)
- A group ring construction of the \([48,24,12\) Type II linear block code]
- Classification of extremal double circulant formally self-dual even codes
- New extremal binary self-dual codes from a modified four circulant construction
- The extended Golay codes considered as ideals
- Weight enumerators of double circulant codes and new extremal self-dual codes
- The Magma algebra system. I: The user language
- Type II codes over \(\mathbb F_4\)
- Group rings, \(G\)-codes and constructions of self-dual and formally self-dual codes
- On the performance of optimal double circulant even codes
- Self-dual codes with an automorphism of order 7 and \(s\)-extremal codes of length 68
- Constructions for self-dual codes induced from group rings
- Bordered constructions of self-dual codes from group rings and new extremal binary self-dual codes
- A new upper bound on the minimal distance of self-dual codes
- Some restrictions on weight enumerators of singly even self-dual codes
- A Group Ring Construction of the Extended Binary Golay Code
- Extremal binary self-dual codes
- Shadow bounds for self-dual codes
- Extremal self-dual codes with an automorphism of order 2
- Type II codes over F/sub 2/+uF/sub 2/
- Algebraic Coding Theory Over Finite Commutative Rings
- New binary coding results by circulants
- Some results on quasi-cyclic codes
- Type II codes over \(\mathbb{F}_4+u\mathbb{F}_4\)