Sarvepalli and Klappenecker showed how classical one-point codes on the Hermitian curve can be used to construct quantum codes. Homma and Kim determined the parameters of a larger family of codes, the two-point codes. In quantum error-correction, the observed presence of asymmetry in some quantum channels led to the study of asymmetric quantum codes (AQECCs) where we no longer assume that the d...

We study the complexity of approximating the VC dimension of a collection of sets, when the sets are encoded succinctly by a small circuit. We show that this problem is • Σp3-hard to approximate to within a factor 2− for any > 0, • approximable in AM to within a factor 2, and • AM-hard to approximate to within a factor N for some constant > 0. To obtain the Σp3-hardness result we solve a random...

The codes obtained as the shortened binary image of linear codes over GF(2m) are studied in detail. Their dimension is computed and it is shown that they may be used as unequal error proteetion codes.

We show how to get a 1-1 correspondence between projective linear codes and 2-weight linear codes. A generalization of the construction gives rise to several new ternary linear codes of dimension six.

Some linear codes associated to maximal algebraic curves via Feng-Rao construction [3] are investigated. In several case, these codes have better minimum distance with respect to the previously known linear codes with same length and dimension.

New spherical codes called laminated spherical codes are constructed in dimensions 2–49 using a technique similar to the construction of laminated lattices. Each spherical code is recursively constructed from existing spherical codes in one lower dimension. Laminated spherical codes outperform the best known spherical codes in the minimum distance sense for many code sizes. The density of a lam...

This work deals with Hadamard Z2Z4Q8-codes, which are binary codes after a Gray map from a subgroup of a direct product of Z2, Z4 and Q8 groups, where Q8 is the quaternionic group. In a previous work, these kind of codes were classified in five shapes. In this paper we analyze the allowable range of values for the rank and dimension of the kernel, which depends on the particular shape of the co...

We consider linear error correcting codes associated to higher-dimensional projective varieties defined over a finite field. The problem of determining the basic parameters of such codes often leads to some interesting and difficult questions in combinatorics and algebraic geometry. This is illustrated by codes associated to Schubert varieties in Grassmannians, called Schubert codes, which have...

Let n; k; d; q]-codes be linear codes of length n, dimension k and minimum Hamming distance d over GF (q). In this paper, eighteen codes are constructed which improve the known lower bounds on minimum distance.