In this note, a class of error-correcting codes is associated to a toric variety defined over a
finite field q, analogous to the class of AG codes associated to a curve. For small q, many of …

This note presents some new information on how the minimum distance of the generalized
toric code corresponding to a fixed set of integer lattice points S⊂ R 2 varies with the base …

From an integral convex polytope in ℝ 2 we give an explicit description of an error-correcting
code over the finite field\Bbb F _q of length (q—1) 2. The codes are obtained from toric …

Toric codes are a class of m-dimensional cyclic codes introduced recently by Hansen
(Coding theory, cryptography and related areas (Guanajuato, 1998), pp 132–142, Springer …

From a rational convex polytope of dimension r⩾ 2 JP Hansen constructed an error
correcting code of length n=(q− 1) r over the finite field Fq. A rational convex polytope is the …

We study subfield-subcodes of Generalized Toric (GT) codes over F p s. These are the
multidimensional analogues of BCH codes, which may be seen as subfield-subcodes of …

We define number-theoretic error-correcting codes based on algebraic number fields,
thereby providing a generalization of Chinese remainder codes akin to the generalization of …

We compute the basic parameters (dimension, length, minimum distance) of affine
evaluation codes defined on a cartesian product of finite sets. Given a sequence of positive …

Error–correcting pairs were introduced in 1988 in the preprint [1] that appeared in [2], and
were found independently in [3], as a general algebraic method of decoding linear codes …

A class of linear codes with good parameters is constructed in this correspondence. It turns
out that linear codes of this class are subcodes of the subfield subcodes of Goppa's …