DYLP is a linear programming code implementing a dynamic simplex algorithm similar to that outlined by Padberg in [5]. The code attempts to maintain a reduced active constraint system by regularly purging loose constraints and variables with unfavourable reduced costs, and adding violated constraints and variables with favourable reduced costs. In abstract, the code alternates between primal an...

Let Fpm be a finite field of cardinality p m and R = Fpm[u]/〈u 〉 = Fpm +uFpm (u = 0), where p is a prime and m is a positive integer. For any λ ∈ Fpm, an explicit representation for all distinct λ-constacyclic codes over R of length pn is given by a canonical form decomposition for each code, where s and n are positive integers satisfying gcd(p, n) = 1. For any such code, using its canonical fo...

The Kneser-Hecke-operator is a linear operator defined on the complex vector space spanned by the equivalence classes of a family of self-dual codes of fixed length. It maps a linear self-dual code C over a finite field to the formal sum of the equivalence classes of those self-dual codes that intersect C in a codimension 1 subspace. The eigenspaces of this self-adjoint linear operator may be d...

We describe and present a new construction method for codes using encodings from group rings. They consist primarily of two types: zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; for example cyclic codes are ideals in the group ring over a cyclic group. The fresh focus is on the encodings themselves, which only under very limited conditions result in idea...

In [22], Kelan Ding and Cunsheng Ding presented a class of linear codes and determined their weight distributions. In this paper, we focus on the generalized Hamming weights of these codes. In order to do so, we study the quadratic forms over subspaces of finite field and obtain some interesting results about subspaces and their dual spaces. On this basis, we solve all the generalized Hamming w...

We introduce and study what we call “completely-extendable conformal intertwining algebras.” Based on results obtained in earlier papers of the author, various examples are given. Duals of these algebras are constructed and nondegenerate such algebras are defined. We prove that the double dual of such a nondegenerate algebra is equal to itself. We explain how these nondegenerate algebras are th...

Toric geometry studies manifolds M2n acted on effectively by a torus of half their dimension, T . Joyce shows that for such a 4-manifold sufficient conditions for a conformal class of metrics on the free part of the action to be self-dual can be given by a pair of linear ODEs and gives criteria for a metric in this class to extend to the degenerate orbits. Joyce and Calderbank-Pedersen use this...

C is self-dual if C = C⊥. We define a Type II code over R as a self-dual code with Eudidean weights divisible by 4k. We consider the natural projection ρ from Z to R, then this map induces the map (also we denote ρ ) from Zn to Rn. We set Λ(C) = 1 √ 2k ρ−1(C). Theorem 1 If C is self-duel code of length n over R, then the lattice Λ(C) is an n-dimensioal unimodular lattice. Moreover if C is Type ...

(in this paper all codes are binary and linear). But, as we shall see in Section III, there exist nontrivial cyclic self-dual codes, the shortest of which has length 14. On the other hand there do not exist doubly-even cyclic self-dual codes, i.e. codes in which all weights are divisible by 4. This is a consequence of Theorem 1. Theorem 1. Suppose C is a binary self-dual code of length n, where...