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Quasi-cyclic dyadic codes in the Walsh-Hadamard transform domain

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2 Author(s)
B. S. Rajan ; Dept. of Electr. Commun. Eng., Indian Inst. of Sci., Bangalore, India ; Moon Ho Lee

A code is s-quasi-cyclic (s-QC) if there is an integer s such that cyclic shift of a codeword by s-positions is also a codeword. For s = 1, cyclic codes are obtained. A dyadic code is a code which is closed under all dyadic shifts. An s-QC dyadic (s-QCD) code is one which is both s-QC and dyadic. QCD codes with s = 1 give codes that are cyclic and dyadic (CD). We obtain a simple characterization of all QCD codes (hence of CD codes) over any field of odd characteristic using Walsh-Hadamard transform defined over that finite field. Also, it is shown that dual a code of an s-QCD code is also an s-QCD code and s-QCD codes for a given dimension are enumerated for all possible values of s.

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IEEE Transactions on Information Theory  (Volume:48 ,  Issue: 8 )