Ultimate linear block and convolutional codes

Linear block and convolutional codes are designed using unit schemes and families of these to required length, rate, distance and type are mined. Properties, such as type and distance, of the codes follow from the types of units used and thus required codes are built from specific units. Orthogonal units, units in group rings, Fourier/Vandermonde units and related units are used to construct and analyse linear block and convolutional codes and to construct these to predefined length, rate, distance and type. Series of self-dual, dual containing, quantum error-correcting and linear complementary dual codes are constructed for both linear block and convolutional codes. Low density parity check linear block and linear convolutional codes are constructed from unit schemes.

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Publication Details

Journal
AIMS Mathematics
Published
2025-01-01
DOI
https://doi.org/10.3934/math.2025387
Citations
1
Primary Topic
Coding theory and cryptography
Type
article
Field-Weighted Citation Impact
2.48
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article

Ultimate linear block and convolutional codes

Ted Hurley
1 citations
AIMS Mathematics
Coding theory and cryptography
2.48
article

Ultimate linear block and convolutional codes

Ted Hurley
article en
1 citations

Abstract

Linear block and convolutional codes are designed using unit schemes and families of these to required length, rate, distance and type are mined. Properties, such as type and distance, of the codes follow from the types of units used and thus required codes are built from specific units. Orthogonal units, units in group rings, Fourier/Vandermonde units and related units are used to construct and analyse linear block and convolutional codes and to construct these to predefined length, rate, distance and type. Series of self-dual, dual containing, quantum error-correcting and linear complementary dual codes are constructed for both linear block and convolutional codes. Low density parity check linear block and linear convolutional codes are constructed from unit schemes.

AIMS MathematicsVol. 10(4)
Ollscoil na Gaillimhe – University of Galway (IE)
Reduced inequalities
Openalex Percentile: Top 11%
Coding theory and cryptography
2.48
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