Related papers: An inductive construction of minimal codes
A minimal code is a linear code where the only instance that a codeword has its support contained in the support of another codeword is when the codewords are scalar multiples of each other. Ashikhmin and Barg gave a sufficient condition…
Integer partitions may be encoded as either ascending or descending compositions for the purposes of systematic generation. Many algorithms exist to generate all descending compositions, yet none have previously been published to generate…
Binary matrix codes with restricted row and column weights are a desirable method of coded modulation for power line communication. In this work, we construct such matrix codes that are obtained as products of affine codes - cosets of…
This paper is devoted to the study of the construction of new quantum MDS codes. Based on constacyclic codes over Fq2 , we derive four new families of quantum MDS codes, one of which is an explicit generalization of the construction given…
It has been known for a long time that $t$-designs can be employed to construct both linear and nonlinear codes and that the codewords of a fixed weight in a code may hold a $t$-design. While a lot of progress in the direction of…
In this paper, we give a new class of reconstructible graphs, which is an extension of my paper `A class of reconstructible graphs'.
We provide a complete classification, in the language of weak-combinatorics, of minimal plus-one generated line arrangements in the complex projective plane with double and triple intersection points.
Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.
We present an inductive method for constructing the basic spin representations of the double covers of the symmetric groups over fields of any characteristic.
We introduce several new constructions of finite posets with the number of linear extensions given by generalized continued fractions. We apply our results to the problem of the minimum number of elements needed for a poset with a given…
An elementary approach to the construction of Coxeter group representations is presented.
We address the problems of constructing quantum convolutional codes (QCCs) and of encoding them. The first construction is a CSS-type construction which allows us to find QCCs of rate 2/4. The second construction yields a quantum…
We determine all majority operations on a four-element set that generate a minimal clone.
We present a simple randomized incremental algorithm for building compressed quadtrees. The resulting algorithm seems to be simpler than previously known algorithms for this task.
Some new infinite families of simple, indecomposable $m$-factorizations of the complete multigraph $\lambda K_v$ are presented. Most of the constructions come from finite geometries.
We give a polynomial representation for additive cyclic codes over $\mathbb{F}_{p^2}$. This representation will be applied to uniquely present each additive cyclic code by at most two generator polynomials. We determine the generator…
As a special class of linear codes, minimal linear codes have important applications in secret sharing and secure two-party computation. Constructing minimal linear codes with new and desirable parameters has been an interesting research…
All components of complements of discriminant varieties of simple real function singularities are explicitly listed. New invariants of such components (for not necessarily simple singularities) are introduced. A combinatorial algorithm…
In this paper, on one hand, a class of linear codes with one or two weights is obtained. Based on these linear codes, we construct two classes of constant composition codes, which includes optimal constant composition codes depending on…
In this paper, by using matrix product codes, several classes of new quantum codes are obtained. Moreover, some of them have better parameters than the previous quantum codes available.