LOW WEIGHT CODEWORDS OF CODES COMING FROM SMOOTH CURVES IN THE HERMITIAN SURFACE

Cyclic Codes: Low-Weight Codewords and Locators

Searching for Low Weight Codewords in Linear Binary Codes

In this work we revisit the known algorithms for searching for low weight codewords in linear binary codes. We propose some improvements on them and also propose a new efficient heuristic.

On the Distribution of Low-Weight Codewords for Turbo Codes

We determine the generating function counting the asymptotic number of (minimal) codewords of low weight for standard parallel concatenated (turbo) code ensembles. We then show that the number of minimal codewords of weight up to some fixed constant follows in the limit of large block lengths a Poisson distribution. In analogy to the standard random graph model, we conjecture that this statemen...

The small weight codewords of the functional codes associated to non-singular Hermitian varieties

This article studies the small weight codewords of the functional code CHerm(X), with X a non-singular Hermitian variety of PG(N, q2). The main result of this article is that the small weight codewords correspond to the intersections of X with the singular Hermitian varieties of PG(N, q2) consisting of q + 1 hyperplanes through a common (N −2)-dimensional space Π, forming a Baer subline in the ...

Minimum distance and the minimum weight codewords of Schubert codes

We consider linear codes associated to Schubert varieties in Grassmannians. A formula for the minimum distance of these codes was conjectured in 2000 and after having been established in various special cases, it was proved in 2008 by Xiang. We give an alternative proof of this formula. Further, we propose a characterization of the minimum weight codewords of Schubert codes by introducing the n...