Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this work we introduce a new generalization of QT codes that we call multi-twisted (MT) codes and study some of their basic properties. Presenting several methods o...

Tables are presented of good ternary and quaternary codes and they are used in the construction of dense sphere packings. Results include 1) tables of the best ternary and quaternary constacyclic codes (including cyclic codes) up to block length 50, 2 ) a class of optimal [ n , 21 codes over GF(q), 3) the ( U + U + w I2u + U I U ) construction, a new ternary code construction technique that can...

Let Fq be a finite field with q elements and denote by θ : Fq → Fq an automorphism of Fq. In this note, we deal with skew constacyclic codes, i.e. linear codes of Fnq which are invariant under the action of a semi-linear map T : Fnq → F n q , defined by T (a0, ..., an−2, an−1) := (αan−1, a0, ..., an−2) for some α ∈ Fq −{0} and n ≥ 2. In particular, we study some algebraic and geometric properti...

Let Fpm be a finite field with cardinality p and R = Fpm + uFpm with u = 0. We aim to determine all α + uβ-constacyclic codes of length np over R, where α, β ∈ Fpm , n, s ∈ N+ and gcd(n, p) = 1. Let α0 ∈ F ∗ pm and α s 0 = α. The residue ring R[x]/〈x np − α − uβ〉 is a chain ring with the maximal ideal 〈x − α0〉 in the case that x n − α0 is irreducible in Fpm[x]. If x−α0 is reducible in Fpm[x], w...