Minimal quadratic residue cyclic codes of length 2n
β Scribed by Sudhir Batra; S. K. Arora
- Publisher
- Springer-Verlag
- Year
- 2005
- Tongue
- English
- Weight
- 194 KB
- Volume
- 18
- Category
- Article
- ISSN
- 1598-5865
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π SIMILAR VOLUMES
In memory of Professor Gian-Carlo Rota for his great contributions in combinatorial and discrete geometry A set of n-tuples over 8 is called a code over 8 or a 8 code if it is a 8 module. A particularly interesting family of 8 -cyclic codes are quadratic residue codes. We define such codes in terms
In this paper we completely describe the 2n#2 minimal cyclic codes of length 2pL over F O , as minimal ideals in the ring R"F O [x]/1xN L !12 in terms of their generating idempotents. Explicit expressions for the primitive idempotents, generating polynomials, minimum distance, and dimension of these
Explicit expressions for the (n Ο© 1) primitive idempotents in FG (the group algebra of the cyclic group G of order p n (p odd prime, n ΟΎ 1) over the finite field F of prime power order q where q is a primitive root modulo p n ) are obtained. The minimum distance, the dimension, and the generating po