Title data
Byrne, Eimear ; Kiermaier, Michael ; Sneyd, Alison:
Properties of codes with two homogeneous weights.
In: Finite Fields and their Applications.
Vol. 18
(2012)
Issue 4
.
 pp. 711727.
ISSN 10715797
DOI: https://doi.org/10.1016/j.ffa.2012.01.002
Project information
Project title: 



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 twoweight codes.
Further data
Item Type:  Article in a journal 

Refereed:  Yes 
Keywords:  ringlinear code; homogeneous weight; weight distribution; twoweight 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 (Computer Algebra) 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:  02 Feb 2022 14:46 
URI:  https://eref.unibayreuth.de/id/eprint/3731 