Related papers: A characterization of two-weight projective cyclic…
We study cyclic codes with arbitrary length over Fp+vFp where theta(v)=av, a in Fp and v^2=0. We characterize all existing codes in case of O(theta)|n by using certain projections from (Fp+vFp)[x;theta] to Fp[x]. We provide an explicit…
Determining the weight distributions of the projective Reed-Muller codes is a very hard problem and has been studied extensively in the literature. In this article, we provide an alternative proof of the second weight of the projective…
We carry out the programme of R. Liouville \cite{Liouville} to construct an explicit local obstruction to the existence of a Levi--Civita connection within a given projective structure $[\Gamma]$ on a surface. The obstruction is of order 5…
A convex projective surface is the quotient of a properly convex open $\Omega$ of $\mathbb{P}(\R)$ by a discret subgroup $\Gamma$ of $\mathrm{SL}_3(\R)$. We give some caracterisations of the fact that a convex projective surface is of…
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…
We explicitly determine the values of reduced cyclotomic periods of order $2^m$, $m\ge 4$, for finite fields of characteristic $p\equiv 3$ or $5\pmod{8}$. These evaluations are applied to obtain explicit factorizations of the corresponding…
Using techniques of projective geometry, we give elementary proofs of two theorems concerning Hagge configurations.
We give an alternative proof of the formula for the minimum distance of a projective Reed-Muller code of an arbitrary order. It leads to a complete characterization of the minimum weight codewords of a projective Reed-Muller code. This is…
Subspace codes have important applications in random network coding. It is interesting to construct subspace codes with both sizes, and the minimum distances are as large as possible. In particular, cyclic constant dimension subspaces codes…
Infinite divisibility of a class of two-dimensional vectors with components in the second Wiener chaos is studied. Necessary and sufficient conditions for infinite divisibility is presented as well as more easily verifiable sufficient…
Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and…
We define the flag space and space of singular vectors for an arrangement A of hyperplanes in projective space equipped with a system of weights a: A --> C. We show that the contravariant bilinear form of the corresponding weighted central…
In this paper, the cyclic codes of length $n$, where $n$ is odd with certain restrictions, over a finite chain ring $R$, have been studied using the structure of group algebra approach. The primitive idempotents of $RG$ of a finite cyclic…
In this paper we study the dual codes of a wide family of evaluation codes on norm-trace curves. We explicitly find out their minimum distance and give a lower bound for the number of their minimum-weight codewords. A general geometric…
We present a number of conditions which are necessary for an n-dimensional projective structure (M,[nabla]) to include the Levi-Civita connection nabla of some metric on M. We provide an algorithm, which effectively checks if a Levi-Civita…
Define an embedding of graph $G=(V,E)$ with $V$ a finite set of distinct points on the unit circle and $E$ the set of line segments connecting the points. Let $V_1,\ldots,V_k$ be a labeled partition of $V$ into equal parts. A 2-factor is…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
A classical result asserts that the complex projective plane modulo complex conjugation is the 4-dimensional sphere. We generalize this result in two directions by considering the projective planes over the normed real division algebras and…
For any q which is a power of 2 we describe a finite subgroup of the group of invertible complex q by q matrices under which the complete weight enumerators of generalized doubly-even self-dual codes over the field with q elements are…
We present constructions and bounds for additive codes over a finite field in terms of their geometric counterpart, i.e., projective systems. It is known that the maximum number of $(h-1)$-spaces in PG$(2,q)$, such that no hyperplane…