We propose a construction of lattices from (skew-) polynomial codes, by endowing quotients some ideals in both number fields and cyclic algebras with suitable trace form. give criteria for unimodularity. This yields integral unimodular multiplicative structure. Examples are provided.

We obtain a tableau definition of the skew Schubert polynomials named by Lascoux, which are defined as flagged double skew Schur functions. These polynomials are in fact Schubert polynomials in two sets of variables indexed by 321-avoiding permutations. From the divided difference definition of the skew Schubert polynomials, we construct a lattice path interpretation based on the Chen-Li-Louck ...

We introduce an additive but not F4-linear map S from Fn4 to F 4 and exhibit some of its interesting structural properties. If C is a linear [n, k, d]4-code, then S(C) is an additive (2n, 2 , 2d)4-code. If C is an additive cyclic code then S(C) is an additive quasi-cyclic code of index 2. Moreover, if C is a module θ-cyclic code, a recently introduced type of code which will be explained below,...

We give an algorithm for generating cyclic self-orthogonal (CSO) codes for an arbitrary positive integer n with gcd(n; q) = 1. Given a cyclic q-ary code of length n, we determine how many codes isomorphic to the given code are cyclic. We introduce a mass formula for CSO(n; q) codes of maximum dimension. Using the mass formula we classify CSO(63; 2) codes. This mass formula works for any cyclic ...

In this paper we prove the universal property of skew PBW extensions generalizing this way the well known universal property of skew polynomial rings. For this, we will show first a result about the existence of this class of non-commutative rings. Skew PBW extensions include as particular examples Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Art...