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Majority Logic Decoding With Subspace Designs

Title data

de la Cruz, Romar ; Wassermann, Alfred:
Majority Logic Decoding With Subspace Designs.
In: IEEE Transactions on Information Theory. Vol. 67 (January 2021) Issue 1 . - pp. 179-186.
ISSN 1557-9654
DOI: https://doi.org/10.1109/TIT.2020.3022683

Abstract in another language

Rudolph (1967) introduced one-step majority logic decoding for linear codes derived from combinatorial designs. The decoder is easily realizable in hardware and requires that the dual code has to contain the blocks of so called geometric designs as codewords. Peterson and Weldon (1972) extended Rudolph’s algorithm to a two-step majority logic decoder correcting the same number of errors as Reed’s celebrated multi-step majority logic decoder. Here, we study the codes from subspace designs. It turns out that these codes have the same majority logic decoding capability as the codes from geometric designs, but their majority logic decoding complexity is sometimes drastically improved. For a known infinite series of subspace designs the reduction of complexity is exponential.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Decoding; Geometry; Linear codes; Parity check codes; Complexity theory; Hardware; Error correction
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics and Didactics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics and Didactics > Chair Mathematics and Didactics - Univ.-Prof. Dr. Volker Ulm
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 29 Jan 2021 07:57
Last Modified: 29 Jan 2021 07:57
URI: https://eref.uni-bayreuth.de/id/eprint/62474