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- Title
Double circulant self-dual and LCD codes over Galois rings.
- Authors
Shi, Minjia; Huang, Daitao; Sok, Lin; Solé, Patrick
- Abstract
This paper investigates the existence, enumeration, and asymptotic performance of self-dual and LCD double circulant codes over Galois rings of characteristic p2 and order p4 with p an odd prime. When p ≡ 3 (mod 4), we give a method to construct a duality preserving bijective Gray map from such a Galois ring to Z2p2. Closed formed enumeration formulas for double circulant codes that are self-dual (resp. LCD) are derived as a function of the length of these codes. Using random coding, we obtain families of asymptotically good self-dual and LCD codes over Zp2 with respect to the metric induced by the standard Fp-valued Gray maps.
- Subjects
CIRCULANT matrices; EXISTENCE theorems; RANDOM variables; CODING theory; GALOIS rings
- Publication
Advances in Mathematics of Communications, 2019, Vol 13, Issue 1, p171
- ISSN
1930-5346
- Publication type
Article
- DOI
10.3934/amc.2019011