Construction of Z4-linear Reed-Muller codes

Details Construction of Z4-linear Reed-Muller codes Construction of Z4-linear Reed-Muller codes

2008-01-19

arxiv.org/abs/0801.3024v1

Computer Science

Information Theory

Paper submitted to IEEE Transactions on Information Theory

Scientific paper

New quaternary Plotkin constructions are given and are used to obtain new families of quaternary codes. The parameters of the obtained codes, such as the length, the dimension and the minimum distance are studied. Using these constructions new families of quaternary Reed-Muller codes are built with the peculiarity that after using the Gray map the obtained Z4-linear codes have the same parameters and fundamental properties as the codes in the usual binary linear Reed-Muller family. To make more evident the duality relationships in the constructed families the concept of Kronecker inner product is introduced.

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