Minimal Codes of Prime-Power Length

Pruthi, Manju; Arora, S. K.

doi:10.1006/ffta.1996.0156

Cited by 53 publications

(27 citation statements)

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“…If t"(m), then m"2, 4, pL, or 2pL for some odd prime p and integer n51 [3, p. 76]. In case m"2, 4, or pL, the explicit expressions for the primitive idempotents are obtained in [4]. Here we consider the case when m"2pL and obtain explicit expressions for the 2n#2 primitive idempotents in R. As a consequence the minimal cyclic codes of length 2pL over F O are obtained as ideals of R. The generating polynomial, the dimension, and the minimum distance for these codes are obtained in Section 3.…”

Section: Introduction Let Fmentioning

confidence: 99%

Minimal Cyclic Codes of Length 2pn

Arora

Pruthi²

1999

Finite Fields and Their Applications

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Section: Introduction Let Fmentioning

confidence: 99%

Minimal Cyclic Codes of Length 2pn

Arora

Pruthi²

1999

Finite Fields and Their Applications

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“…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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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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“…(2) For each odd with | 2 , the number of irreducible polynomials of degree is ( )/ ⋅ gcd( , − 1), and the number irreducible polynomials of degree 2 is…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…(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%