All two-weight irreducible cyclic codes?
type: Item
instance of: scholarly article
title: All two-weight irreducible cyclic codes?
zbMATH Open document ID: 1023.94016
author: Bernhard Schmidt
author: Clinton White
published in: Finite Fields and their Applications
publication date: 2002-07-04T00:00:00Z
review text: The authors obtain necessary and sufficient conditions for an irreducible cyclic code to have at most two weights, and it is done without evaluating the corresponding Gauss sums in McEliece's identity. Their approach enables a unified explanation for all known two-weight irreducible codes, and it gives four new sporadic examples. The authors conjecture that there are no other two-weight irreducible cyclic codes and give a partial proof of this conjecture conditionally on the generalized Riemann hypothesis.
Mathematics Subject Classification ID: 94B15
zbMATH DE Number: 1763658
zbMATH Keywords: irreducible cyclic codes
zbMATH Keywords: class number
zbMATH Keywords: generalized Riemann hypothesis
reviewed by: Nikolai L. Manev
MaRDI profile type: Publication
full work available at URL: ffta.2000.0293
OpenAlex ID: W2064494467
cites work: Some sets of type \((m,n)\) in cubic order planes
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cites work: Coding theory
cites work: Q5690489
DOI: 10.1006/FFTA.2000.0293
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description: scientific article; zbMATH DE number 1763658