DWE: Discriminating Word Enumerator

Toward the Weight Enumerator Function of Pseudo-codewords

Complete weight enumerators of a family of three-weight linear codes

Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime p, we present the explicit complete weight enumerator of a family of p-ary linear codes constructed with defining set. The weight enumerator is an immediate result of the complete weight enumerator which shows that the codes proposed in this paper are three-weight linear codes...

The Partition Weight Enumerator and Bounds on Mds Codes

Maximum Distance Separable (MDS) codes are those error correction codes that meet the singleton bound, thus they have the largest minimum distance possible. The main research problem is to find an upper bound on the length of the codewords when the alphabet size and dimension of the code are fixed. This paper will present a new technique using the Partition Weight Enumerator for solving this pr...

Rational Point Counts for del Pezzo Surfaces over Finite Fields and Coding Theory

The goal of this thesis is to apply an approach due to Elkies to study the distribution of rational point counts for certain families of curves and surfaces over finite fields. A vector space of polynomials over a fixed finite field Fq gives rise to a linear code, and the weight enumerator of this code gives information about point count distributions. The MacWilliams theorem gives a relation b...

Information-bit error rate and false positives in an MDS code

In this paper, a computation of the inputredundancy weight enumerator is presented. This is used to improve the theoretical approximation of the information–bit and –symbol error rate, in terms of the channel bit-error rate, in a block transmission through a discrete memoryless channel. Since a bounded distance reproducing encoder is assumed, the computation of the here-called false positive (a...