Ultimate linear block and convolutional codes
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. Orth...
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Zusammenfassung: | 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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DOI: | 10.48550/arxiv.2403.01491 |