The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes

Roger Hammons, A.; Vijay Kumar, P.; Calderbank, A.R.; J. A. Sloane, N.; Solé, Patrick

doi:10.1109/18.312154

Public

The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes

Published in IEEE Transactions on Information Theory • Mar 1, 1994

Authors:

A. Roger Hammons

P. Vijay Kumar

A.R. Calderbank

Abstract

Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by Nordstrom-Robinson (1967), Kerdock (1972), Preparata (1968), Goethals (1974), and Delsarte-Goethals (1975). It is shown here that all these codes can be very simply cons...

Subject

Linear code

Combinatorics

Hamming code

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