Minimal Cyclic Codes of Length 2pn

Arora, S. K.; Pruthi, Manju

doi:10.1006/ffta.1998.0238

Cited by 45 publications

(26 citation statements)

References 2 publications

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“…We obtain the explicit expressions for the primitive idempotents of these codes (see Theorem 4.2) by using the approach presented in [3] and give a simple version of the main result (i.e., Theorem 2.6) of [2] (see Theorem 3.3).…”

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confidence: 99%

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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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confidence: 99%

“…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].…”

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confidence: 99%

Some cyclic codes of length 2p n

Batra¹,

Arora

2010

Des. Codes Cryptogr.

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“…By Lemma 1, the number of irreducible factors of − 1, which coincides with the number of primitive idempotents in , is 1 …”

Section: Primitive Idempotents Inmentioning

confidence: 91%

“…(1) In [1,2], = 2, 4, , and 2 , where is an odd prime and is a primitive root modulo . (2) In [3,4], = 2 , ≥ 3.…”

Section: Introductionmentioning

confidence: 99%

Primitive Idempotents of Irreducible Cyclic Codes of Length n

Lin

Yue

2018

Mathematical Problems in Engineering

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“…Then F G, the group algebra of the cyclic group G over F , is semi-simple and has only a finite number of primitive idempotents which equals the number of cyclotomic cosets modulo m. Let t be the multiplicative order of q modulo m, then 1 ≤ t ≤ φ(m) [4]. If t = φ(m) and m = 2, 4, p n , 2p n , the complete sets of primitive idempotents were calculated by Pruthi and Arora [1,6]. The minimal quadratic residue cyclic codes of length p n were obtained by Batra and Arora [3].…”

Section: Introductionmentioning

confidence: 99%