New Results on the Pseudoredundancy

TL;DR

This paper investigates the pseudoredundancy of binary linear codes, providing new bounds and exact values for various code classes, which enhances understanding of their pseudoweight properties in LDPC code analysis.

Contribution

It introduces new results on pseudoredundancy using value assignment, including bounds and exact calculations for specific code families.

Findings

Derived upper bounds for pseudoredundancy of certain codes

Computed exact pseudoredundancy for specific k-dimensional codes

Analyzed effects of coordinate repetition and shortening on pseudoredundancy

Abstract

The concepts of pseudocodeword and pseudoweight play a fundamental role in the finite-length analysis of LDPC codes. The pseudoredundancy of a binary linear code is defined as the minimum number of rows in a parity-check matrix such that the corresponding minimum pseudoweight equals its minimum Hamming distance. By using the value assignment of Chen and Kl{\o}ve we present new results on the pseudocodeword redundancy of binary linear codes. In particular, we give several upper bounds on the pseudoredundancies of certain codes with repeated and added coordinates and of certain shortened subcodes. We also investigate several kinds of k-dimensional binary codes and compute their exact pseudocodeword redundancy.