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Extremal Type I --Codes and --Frames of Odd Unimodular Lattices | IEEE Journals & Magazine | IEEE Xplore

Extremal Type I \mathbb {Z}_{k} -Codes and k -Frames of Odd Unimodular Lattices

Publisher: IEEE

Abstract:

For some extremal (optimal) odd unimodular lattice L in dimensions 12, 16, 20, 28, 32, 36, 40, and 44, we determine all integers k such that L contains a k-frame. This re...View more

Abstract:

For some extremal (optimal) odd unimodular lattice L in dimensions 12, 16, 20, 28, 32, 36, 40, and 44, we determine all integers k such that L contains a k-frame. This result yields the existence of an extremal Type I Z k -code of lengths 12, 16, 20, 32, 36, 40, and 44, and a near-extremal Type I Z k -code of length 28 for positive integers k with only a few exceptions.
Published in: IEEE Transactions on Information Theory ( Volume: 61, Issue: 1, January 2015)
Page(s): 72 - 81
Date of Publication: 20 November 2014

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Publisher: IEEE

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