Binary transmission codes with higher order spectral zeros at zero frequency
IEEE Transactions on Information Theory
Coding Techniques for Digital Recorders
Coding Techniques for Digital Recorders
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Kth order zero disparity codes have been consideredin several recent papers. In the first part of this paper weremove the zero disparity condition and consider the larger classof codes, Kth order disparity Dcodes. We establish properties of disparity D codesshowing that they have many of the properties of zero disparitycodes. We give existence criteria for them, and discuss how newcodewords may be formed from ones already known. We then discussKth order disparity D codes thathave the same number of codewords. We discuss the minimum distanceproperties of these new codes and present a decoding algorithmfor them. In the second part of the paper we look at how theminimum distance of disparity D codes can be improved.We consider subsets of a very specialised subclass, namely firstorder zero disparity codes over alphabet Aq ofsize q. These particular subsets have qcodewords of length n and minimum Hamming distancen. We show that such a subset exists when qis even and nis a multiple of 4, andalso when q is odd and n is even.These subsets have the best error correction capabilities ofany subset of q first order zero disparity codewords.