The Geometry of Homogeneous Two-Weight Codes
Thomas Honold
TL;DR
This paper extends the theory of linear homogeneous two-weight codes over finite Frobenius rings, showing their connection to strongly regular graphs and introducing dual codes and graphs similar to classical finite field cases.
Contribution
It generalizes previous results by linking non-projective two-weight codes to strongly regular graphs and defining dual codes and graphs over Frobenius rings.
Findings
Non-projective two-weight codes give rise to strongly regular graphs.
Dual two-weight codes and associated graphs are constructed over Frobenius rings.
Extensions of classical finite field results to Frobenius ring settings.
Abstract
The results of [1,2] on linear homogeneous two-weight codes over finite Frobenius rings are exended in two ways: It is shown that certain non-projective two-weight codes give rise to strongly regular graphs in the way described in [1,2]. Secondly, these codes are used to define a dual two-weight code and strongly regular graph similar to the classical case of projective linear two-weight codes over finite fields [3].
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · graph theory and CDMA systems