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Properties of codes with two homogeneous weights

Title data

Byrne, Eimear ; Kiermaier, Michael ; Sneyd, Alison:
Properties of codes with two homogeneous weights.
In: Finite Fields and their Applications. Vol. 18 (July 2012) Issue 4 . - pp. 711-727.
ISSN 1071-5797
DOI: https://doi.org/10.1016/j.ffa.2012.01.002

Project information

Project title:
Project's official titleProject's id
Konstruktive Methoden in der algebraischen Codierungstheorie für lineare Codes über endlichen Kettenringen.WA-1666/4

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

Delsarte showed that for any projective linear code over a finite field 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 regular projective linear code C over a finite Frobenius ring with two integral nonzero homogeneous weights w₁ < w₂ there is a positive integer d, a divisor of |C|, and positive integer u such that w₁ = du and w₂ = d(u+1). This gives a new proof of the known result that any such code yields a strongly regular graph. We apply these results to existence questions on two-weight codes.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: ring-linear code; homogeneous weight; weight distribution; two-weight code; character module; strongly regular graph; Cayley graph
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 20 Nov 2014 08:27
Last Modified: 20 Feb 2015 11:17
URI: https://eref.uni-bayreuth.de/id/eprint/3731