3 papers
cs.IT2026
Dualities for finite abelian groups and applications to coding theory
Jay A. Wood
The choice of an isomorphism, a duality, between a finite abelian group and its character group allows one to define dual codes of additive codes over . Properties of dualit…
cs.IT2026
Weights on finite fields and failures of the MacWilliams identities
Jay A. Wood
In the 1960s, MacWilliams proved that the Hamming weight enumerator of a linear code over a finite field completely determines, and is determined by, the Hamming weight enumerator…
math.RA2024
Weights with Maximal Symmetry and Failures of the MacWilliams Identities
Jay A. Wood
This paper examines the -weight enumerators of weights with maximal symmetry over finite chain rings and matrix rings over finite fields. In many cases, including the homoge…