Monomial codes under linear algebra point of view

2023/04/01 by Mouloua, El Mahdi, Najmeddine, Mustapha, Garcia-Planas, Maria Isabel +1
#94B15 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2304.00398

Abstract

The monomial codes over a Galois field F_q that can be thought invariant subspaces are essential to us in this study. More specifically, we look into the link between monomial codes and characteristic subspaces and the decomposition of monomial codes into minimal invariant subspaces. Additionally, we study some of the characteristics of monomial codes and generalize them by proposing the idea of generalized monomial codes.

Related

• Monomial-like codes
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• Generalized weights of codes over rings and invariants of monomial ideals
• On the equivalence of linear cyclic and constacyclic codes
• Characteristics of Invariant Weights Related to Code Equivalence over\n Rings