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...

We show how cyclic (f, σ, δ)-codes over finite rings canonically induce a Z-lattice in R N. The construction can be viewed as a generalization of the classical Construction A for lattices from linear codes and has applications to coset coding, in particular to wire-tap coding. Previous results for lattices obtained from σ-constacyclic codes by Ducoat and Oggier are obtained as special cases.

Polycyclic codes are a generalization of cyclic and constacyclic codes. Even though they have been known since 1972 received some attention more recently, there not many studies on polycyclic This paper presents an in-depth investigation associated with trinomials. Our results include number facts about trinomials, properties codes, new quantum derived from We also state several conjectures pol...

In this note we determine weight distributions of minimal constacyclic codes of length p over the finite field Fl, where p is a prime which is coprime to l.

Recently, a new algorithm to test equivalence of two cyclic codes has been introduced which is efficient and produced useful results. In this work, we generalize constacyclic codes. As an application the found many with good parameters properties. particular, 22 that improve minimum distances best known linear (BKLCs).

We mainly investigate the structures of skew cyclic and skew quasicyclic codes of arbitrary length over Galois rings. Similar to [5], our results show that the skew cyclic codes are equivalent to either cyclic and quasi-cyclic codes over Galois rings. Moreover, we give a necessary and sufficient condition for skew cyclic codes over Galois rings to be free. A sufficient condition for 1-generator...