Idempotents in group algebras and minimal abelian codes

“…While computing idempotent generators of the minimal abelian codes over a finite field, Ferraz and Milies [11] gave a simple method of computing the results obtained in [2,15].…”

mentioning

confidence: 99%

Some cyclic codes of length 2p n

Batra¹,

Arora

2010

Des. Codes Cryptogr.

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Explicit expressions for 4n + 2 primitive idempotents in the semi-simple group ring R 2 p n ≡ G F(q) [x] are obtained, where p and q are distinct odd primes; n ≥ 1 is an integer and q has order φ(2 p n ) 2 modulo 2 p n . The generator polynomials, the dimension, the minimum distance of the minimal cyclic codes of length 2 p n generated by these 4n + 2 primitive idempotents are discussed. For n = 1, the properties of some (2 p, p) cyclic codes, containing the above minimal cyclic codes are analyzed in particular. The minimum weight of some subset of each of these (2 p, p) codes are observed to satisfy a square root bound.

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“…By applying the rule that μ s,t is equal to the sum of the s-powers of the zeros of P −1 t (x) we find for the idempotent table M 20,3,−1 , the rows of which are indexed respectively by 0, 1, 2, 4, 11, 5 and the columns by 0, 2, 3, 6, 12, 5. For more examples of primitive idempotents of constacyclic and negacyclic codes we refer to [10,16,22,[26][27][28].…”

Section: Proof (I) and (Ii) Follow Immediately From Theorem 19mentioning

confidence: 99%

Primitive idempotent tables of cyclic and constacyclic codes

Zanten

2018

Des. Codes Cryptogr.

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Idempotents in group algebras and minimal abelian codes

Cited by 67 publications

References 6 publications

Explicit idempotents of finite group algebras

Explicit idempotents of finite group algebras

Some cyclic codes of length 2p n

Primitive idempotent tables of cyclic and constacyclic codes

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