The Cyclotomic Problem

Katre, S. A.

doi:10.1007/978-93-86279-09-5_5

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Minimal Codes For the Group C P R × C P N1

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2004

2024

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Cited by 4 publications

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“…0 otherwise, and where A ij 's are cyclotomic numbers, which are known in terms of Jacobi sums (see [8,19]) and for all small values of e, also see [17,Part 1]. Let C = (c i,j ) e×e be the e × e integral matrix given by…”

Section: Minimal Codes For the Group C P R × C P Nmentioning

confidence: 99%

Explicit Determination of Certain Minimal Abelian Codes and Their Minimum Distances

Grover

Bhandari

2012

Asian-European J. Math.

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In this paper minimal codes for several classes of non-cyclic abelian groups have been constructed by explicitly determining a complete set of primitive idempotents in the corresponding group algebras. Some classes of non-p-groups have also been considered. The minimum distances of such abelian codes have been discussed and compared to the minimum distances of cyclic codes of same lengths and dimensions over the same field.

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Section: Minimal Codes For the Group C P R × C P Nmentioning

confidence: 99%

Explicit Determination of Certain Minimal Abelian Codes and Their Minimum Distances

Grover

Bhandari

2012

Asian-European J. Math.

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Zeta function of the projective curveaY 21 =bX 21 +cZ 21 over a class of finite fields, for odd primesl

Anuradha

2005

Proc. Math. Sci.

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Cyclotomic numbers and primitive idempotents in the ring GF(q)[x]/(xpn−1)

Sharma

Bakshi

Dumir

et al. 2004

Finite Fields and Their Applications

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Let q be an odd prime power and p be an odd prime with gcdðp; qÞ ¼ 1: Let order of q modulo p be f ; gcdð pÀ1 f ; qÞ ¼ 1 and q f ¼ 1 þ pl: Here expressions for all the primitive idempotents in the ring R p n ¼ GF ðqÞ½x=ðx p n À 1Þ; for any positive integer n; are obtained in terms of cyclotomic numbers, provided p does not divide l if nX2: The dimension, generating polynomials and minimum distances of minimal cyclic codes of length p n over GF ðqÞ are also discussed. r 2004 Elsevier Inc. All rights reserved.

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The Cyclotomic Problem

Cited by 4 publications

References 15 publications

Explicit Determination of Certain Minimal Abelian Codes and Their Minimum Distances

Explicit Determination of Certain Minimal Abelian Codes and Their Minimum Distances

Zeta function of the projective curveaY 21 =bX 21 +cZ 21 over a class of finite fields, for odd primesl

Cyclotomic numbers and primitive idempotents in the ring GF(q)[x]/(xpn−1)

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