Self-dual cyclic and quantum codes over ℤ2 × (ℤ2 + uℤ2)

In this paper, we introduce self-dual cyclic codes over the ring [Formula: see text]. We determine the conditions for any [Formula: see text]-cyclic code to be self-dual, that is, [Formula: see text]. Since the binary image of a self-orthogonal [Formula: see text]-linear code is also a self-orthogonal binary linear code, we introduce quantum codes over [Formula: see text]. Finally, we present some examples of self-dual cyclic and quantum codes that have good parameters.

Computing coset leaders and leader codewords of binary codes

In this paper we use the Gröbner representation of a binary linear code [Formula: see text] to give efficient algorithms for computing the whole set of coset leaders, denoted by [Formula: see text] and the set of leader codewords, denoted by [Formula: see text]. The first algorithm could be adapted to provide not only the Newton and the covering radius of [Formula: see text] but also to determine the coset leader weight distribution. Moreover, providing the set of leader codewords we have a test-set for decoding by a gradient-like decoding algorithm. Another contribution of this article is the relation established between zero neighbors and leader codewords.

Representations of Code Vertex Operator Superalgebras

We study the representations of code vertex operator superalgebras resulting from a binary linear code which contains codewords of odd weight. We also show that there exists only one set of seven mutually orthogonal conformal vectors with central charge 1/2 in the Hamming code vertex operator superalgebra [Formula: see text]. Furthermore, we classify all the irreducible weak [Formula: see text]-modules.