Abstract
© 2016 Elsevier Inc. All rights reserved. We give an algebraic structure for a large family of binary quasi-cyclic codes. We construct a family of commutative rings and a canonical Gray map such that cyclic codes over this family of rings produce quasi-cyclic codes of arbitrary index in the Hamming space via the Gray map. We use the Gray map to produce optimal linear codes that are quasi-cyclic.
Original language | English |
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Pages (from-to) | 138-149 |
Journal | Finite Fields and Their Applications |
Volume | 40 |
DOIs | |
Publication status | Published - 1 Jul 2016 |
Keywords
- Codes over rings
- Quasi-cyclic codes