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

نویسندگان

  • Eimear Byrne
  • Marcus Greferath
  • Thomas Honold
چکیده

It is known that a linear two-weight code C over a finite field Fq corresponds both to a multiset 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 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.

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عنوان ژورنال:
  • Des. Codes Cryptography

دوره 48  شماره 

صفحات  -

تاریخ انتشار 2008