Published January 1, 2017
| Version v1
Journal article
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Structure and performance of generalized quasi-cyclic codes
Creators
- 1. Sabanci Univ, Istanbul, Turkey
- 2. Middle East Tech Univ, Ankara, Turkey
- 3. Ferdowsi Univ Mashhad, Dept Pure Math, Mashhad, Iran
- 4. Univ Paris 08, CNRS, LAGA, F-93526 St Denis, France
Description
Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder Theorem yields a decomposition of GQC codes into a sum of concatenated codes. This decomposition leads to a trace formula, a minimum distance bound, and to a criteria for the GQC code to be self-dual or to be linear complementary dual (LCD). Explicit long GQC codes that are LCD, but not QC, are exhibited. (C) 2017 Elsevier Inc. All rights reserved.
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