Ring geometries, Two-Weight Codes and Strongly Regular Graphs

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dc.creatorByrne, E.
dc.creatorGreferath, M.
dc.creatorHonold, T.
dc.date2007-09-06
dc.date.accessioned2026-07-07T08:27:56Z
dc.date.available2026-07-07T08:27:56Z
dc.descriptionIt is known that a linear two-weight code $C$ over a finite field $\F_q$ corresponds both to a multiset in a projective space over $\F_q$ that meets every hyperplane in either $a$ or $b$ points for some integers $a<b$, and to a strongly regular graph whose vertices may be identified with the codewords of $C$. Here we extend this classical result to the case of a ring-linear code with exactly two nonzero homogeneous weights and multisets of points in an associated projective ring geometry. We will show that a two-weight code over a finite Frobenius ring gives rise to a strongly regular graph, and we will give some constructions of two-weight codes using ring geometries. These examples all yield infinite families of strongly regular graphs with non-trivial parameters.
dc.descriptionto appear in Designs Codes and Cryptography
dc.identifierhttps://arxiv.org/abs/0709.0862
dc.identifierhttp://arxiv.org/abs/0709.0862
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137444
dc.subjectCombinatorics
dc.subjectGeneral Mathematics
dc.subjectRings and Algebras
dc.titleRing geometries, Two-Weight Codes and Strongly Regular Graphs
dc.typetext

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