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Ultimate linear block and convolutional codes (2403.01491v6)

Published 3 Mar 2024 in cs.IT, math.IT, and math.RA

Abstract: Codes considered as structures within unit schemes greatly extends the availability of linear block and convolutional codes and allows the construction of these codes to required length, rate, distance and type. Properties of a code emanate from properties of the unit from which it was derived. 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. 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 convolutional codes are constructed with no short cycles in the control matrix.

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