Abstract
Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra \(\mathbb{F}[x]/(x^n-1)\), where \(\mathbb{F}\) is a finite field. A particular choice of the data leads to the class of doubly-cyclic CC’s. Within this large class Reed-Solomon and BCH convolutional codes can be defined. After constructing doubly-cyclic CC’s, basic properties are derived on the basis of which distance properties of Reed-Solomon convolutional codes are investigated. This shows that some of them are optimal or near optimal with respect to distance and performance.
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Gluesing-Luerssen, H., Schmale, W. On Doubly-Cyclic Convolutional Codes. AAECC 17, 151–170 (2006). https://doi.org/10.1007/s00200-006-0014-9
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DOI: https://doi.org/10.1007/s00200-006-0014-9