One-Sided k-Orthogonal Matrices Over Finite Semi-Local Rings And Their Codes

03/09/2021

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by   Virgilio P. Sison, et al.

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Let R be a finite commutative ring with unity 1_R and k ∈ R. Properties of one-sided k-orthogonal n × n matrices over R are presented. When k is idempotent, these matrices form a semigroup structure. Consequently new families of matrix semigroups over certain finite semi-local rings are constructed. When k=1_R, the classical orthogonal group of degree n is obtained. It is proved that, if R is a semi-local ring, then these semigroups are isomorphic to a finite product of k-orthogonal semigroups over fields. Finally, the antiorthogonal and self-orthogonal matrices that give rise to leading-systematic self-dual or weakly self-dual linear codes are discussed.