Maximum distance codes over rings of order 4

TL;DR: In this article, a class of skew cyclic codes over the ring of skew polynomial rings with an automorphism and a derivation of the multiplication matrix was studied.

TL;DR: The rank for cyclic codes of an arbitrary length n over the ringZ-2 is studied, and the minimal spanning sets for these codes are found.

TL;DR: The purpose of this short chapter is to study codes over ZprZpr satisfying two distinct Singleton type bounds, in preparation of the Chapter 13.

TL;DR: Certain notorious nonlinear binary codes contain more codewords than any known linear code and can be very simply constructed as binary images under the Gray map of linear codes over Z/sub 4/, the integers mod 4 (although this requires a slight modification of the Preparata and Goethals codes).

TL;DR: In this paper, it was shown that all the nonlinear binary codes constructed by Nordstrom-Robinson, Kerdock, Preparata, Goethals, and Delsarte-Goethals can be constructed as binary images under the Gray map of linear codes over Z_4, the integers mod 4.

TL;DR: In this paper, the alphabet F/sub 2/uF/sub/2/1/2 is viewed as a quotient of the Gaussian integers by the ideal (2), and self-dual codes with Lee weights a multiple of 4 are called Type II.

TL;DR: Using invariant theory, a basis is given for the space of invariants to which belongs the three variables weight enumerator of a self-dual code, and a general bound for the weight of such codes is derived.