@article{Hurley2025, 
author = {Ted Hurley},
title = {Ultimate linear block and convolutional codes},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {4},
pages = {8398-8421},
keywords = {code, linear, convolutional, self-dual, dual-containing, quantum code, complementary dual, LDPC},
url = {https://www.sciopen.com/article/10.3934/math.2025387},
doi = {10.3934/math.2025387},
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.}
}