Introduction

This chapter describes those functions which are applicable to linear codes over Z_4. Codes over general finite rings (including Galois rings) will be supported in the future, but currently only Z_4-codes are supported. The basic facilities for Z_4-codes presented here will also be extended in the near future.

For modules defined over rings with zero divisors, such as Z_4, it is of course not possible to talk about the concept of dimension (the modules are not free). But in Magma each code over such a ring has a unique generator matrix with k rows, and we will call k the pseudo-dimension of the code. Since k is unique for each code, we will retain the notation of a [n, k]-linear code. Note that the rank of the generator matrix is always well-defined and unique (based on the Smith form which is well-defined over PIRs), but k may sometimes be larger than the rank.

In this chapter, as for codes over finite fields, the term "code" will refer to a linear code, unless otherwise specified.

The reader is referred to [Wan97] as a general reference on Z_4-codes. Thanks are also expressed to Graham Norton for advice and help in the development of Z_4-codes in Magma.