2007•IEEE Transactions on Information TheoryRequires access

New Quasi-Cyclic Codes From Simplex Codes

Eric Z. Chen

Abstract

As a generalization of cyclic codes, quasi-cyclic (QC) codes contain many good linear codes. But quasi-cyclic codes studied so far are mainly limited to one generator (1-generator) QC codes. In this correspondence, 2-generator and 3-generator QC codes are studied, and many good, new QC codes are constructed from simplex codes. Some new binary QC codes or related codes, that improve the bounds on maximum minimum distance for binary linear codes are constructed. They are 5-generator QC [93,17,34] and [254,23,102] codes, and related [96,17,36], [256,23,104] codes

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Key concepts: Linear code, Block code, Expander code, Luby transform code, Reed–Muller code, Concatenated error correction code, Raptor code, Tornado code