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Distance regularity of Kerdock codes. (Russian, English) Zbl 1155.94414
Sib. Mat. Zh. 49, No. 3, 668-681 (2008); translation in Sib. Math. J. 49, No. 3, 539-548 (2008).
Summary: A code is called distance regular, if for every two codewords \(x\), \(y\) and integers \(i\), \(j\) the number of codewords \(z\) such that \(d(x,z)=i\) and \(d(y,z)=j\), with \(d\) the Hamming distance, does not depend on the choice of \(x\), \(y\) and depends only on \(d(x,y)\) and \(i\), \(j\). Using some properties of the discrete Fourier transform we give a new combinatorial proof of the distance regularity of an arbitrary Kerdock code. We also calculate the parameters of the distance regularity of a Kerdock code.

MSC:
94B65 Bounds on codes
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