A class of one-dimensional MDS convolutional codes

Details A class of one-dimensional MDS convolutional codes A class of one-dimensional MDS convolutional codes

2004-12-17

arxiv.org/abs/cs/0412085v1

Computer Science

Information Theory

20 pages

Scientific paper

A class of one-dimensional convolutional codes will be presented. They are all MDS codes, i. e., have the largest distance among all one-dimensional codes of the same length n and overall constraint length delta. Furthermore, their extended row distances are computed, and they increase with slope n-delta. In certain cases of the algebraic parameters, we will also derive parity check matrices of Vandermonde type for these codes. Finally, cyclicity in the convolutional sense will be discussed for our class of codes. It will turn out that they are cyclic if and only if the field element used in the generator matrix has order n. This can be regarded as a generalization of the block code case.

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