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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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