Ring geometries, two-weight codes, and strongly regular graphs

Eimear Byrne, Marcus Greferath, Thomas Honold

Research output: Contribution to journalArticleScientificpeer-review

21 Citations (Scopus)

Abstract

It is known that a projective linear two-weight code C over a finite field Fq corresponds both to a set of points in a projective space over Fq 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 sets of points in an associated projective ring geometry. We will introduce regular projective two-weight codes over finite Frobenius rings, we will show that such a code gives rise to a strongly regular graph, and we will give some constructions of two-weight codes using ring geometries. All these examples yield infinite families of strongly regular graphs with non-trivial parameters.
Original languageUndefined/Unknown
Pages (from-to)1-16
Number of pages16
JournalDESIGNS CODES AND CRYPTOGRAPHY
Volume48
Issue number1
DOIs
Publication statusPublished - 2008
MoE publication typeA1 Journal article-refereed

Keywords

  • ring-linear codes
  • two-weight codes
  • strongly regular graphs
  • homogeneous weights
  • Frobenius rings

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