Existence of certain class of duadic group algebra codes |
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| Institution: | 1. Division of Plastic Surgery, MetroHealth, 2500 Metrohealth Drive, Cleveland, OH 44109, United States;2. Department of Plastic Surgery, Cleveland Clinic, Cleveland, OH, United States |
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| Abstract: | Duadic codes are defined in terms of idempotents of a group algebra GF(q)G, where G is a finite group and gcd(q,|G|)=1. Under the conditions of (1) q=2m, and (2) the idempotents are taken to be central and (3) the splitting is μ−1, we show that such duadic codes exist if and only if q has odd-order modulo |G|. |
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