TL;DR
This paper explores non-projective two-weight codes and shows that their weight differences follow a specific mathematical pattern under certain conditions.
Contribution
The paper extends the known result about weight differences in two-weight codes to non-projective cases with mild conditions.
Findings
The difference of non-zero weights in non-projective two-weight codes is a power of the field's characteristic under mild conditions.
Exhaustive enumerations of feasible parameters are provided for small dimensions in the binary case.
Abstract
It has been known since the 1970’s that the difference of the non-zero weights of a projective Fq-linear two-weight code has to be a power of the characteristic of the underlying field. Here, we study non-projective two-weight codes and, e.g., show the same result under mild extra conditions. For small dimensions we give exhaustive enumerations of the feasible parameters in the binary case.
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · graph theory and CDMA systems