101. On the Parameters of Codes with Two Homogeneous Weights
- Author
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Byrne, Eimear, Sneyd, Alison, and Saadi, Assia
- Subjects
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM] ,[MATH.MATH-IT] Mathematics [math]/Information Theory [math.IT] ,[INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT] ,[INFO.INFO-CR] Computer Science [cs]/Cryptography and Security [cs.CR] - Abstract
Delsarte showed that for any projective linear code over a nite eld GF(pr) with two nonzero Hamming weights w1 < w2 there exist positive integers u and s such that w1 = psu and w2 = ps(u + 1). Moreover, he showed that the additive group of such a code has a strongly regular Cayley graph. Here we show that for any proper, regular, projective linear code C over a nite Frobenius ring with two integral nonzero homogeneous weights w1 < w2 there is a positive integer d, a divisor of jCj, and positive integer u such that w1 = du and w2 = d(u+1). In doing so, we present a new proof that any such code yields a strongly regular graph.
- Published
- 2011