Linear cyclic codes of wordlength v over GF(q s ) which are also linear cyclic codes of wordlength sv over GF(q)

Abstract

Any nonsingular linear transformation φ: GF(qs) → GF(qs) can be used to treat a linear cyclic code ρ of wordlength v over GF(qs) as a linear code φ(ρ) of Wordlength sv over GF(q). This paper determines those linear cyclic codes ρ and transformations φ for which the resulting linear code φ(ρ) is also cyclic.