Constacyclic $$F_q$$ F q -linear codes over $$F_{q^l}$$ F q l

Abstract

Let $$F_q$$Fq be a finite field of order $$q$$q, $$l$$l a prime, $$\lambda \in F_q^{\times }=F_q-\{0\}$$??Fq×=Fq-{0} and $$F_{q^l}$$Fql an extension field of $$F_q$$Fq with degree $$l$$l. First, the structure and a canonical form decomposition of any $$\lambda $$?-constacyclic $$F_q$$Fq-linear code over $$F_{q^l}$$Fql are presented. By use of this decomposition, enumeration, construction, encoder and dual codes of these codes are investigated. Then self-orthogonal and self-dual negacyclic $$F_q$$Fq-linear codes over $$F_{q^l}$$Fql are studied, and a precisely expression for self-dual negacyclic $$F_q$$Fq-linear codes over $$F_{q^2}$$Fq2 is obtained.