2011/03/18 by Jens Zumbrägel, Zumbrägel, Jens, Vitaly Skachek +3
Computer Science · Engineering · Mathematics · #Advanced Wireless Communication Techniques #Coding theory and cryptography #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1103.3641
14 pages. arXiv admin note: substantial text overlap with arXiv:1005.3486
openalex publication_date 2011/03/18 · arxiv created 2012/03/06 · arxiv updated 2012/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The AWGNC, BSC, and max-fractional pseudocodeword redundancies of a binary linear code are defined to be the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the minimum Hamming distance of the code. It is shown that most codes do not have a finite pseudocodeword redundancy. Also, upper bounds on the pseudocodeword redundancy for some families of codes, including codes based on designs, are provided. The pseudocodeword redundancies for all codes of small length (at most 9) are computed. Furthermore, comprehensive results are provided on the cases of cyclic codes of length at most 250 for which the eigenvalue bound of Vontobel and Koetter is sharp.