DIMACS TR: 93-50

A Linear Construction for Certain Kerdock and Preparata Codes

Authors: A.R.Calderbank, A.R.Hammons, Jr., P. Vijay Kumar, N. J. A. Sloane, and Patrick Sole


The Nordstrom-Robinson, Kerdock and (slightly modified) Preparata codes are shown to be linear over Z sub 4, the integers mod 4. The Kerdock and Preparata codes are duals over Z sub 4, and the Nordstrom-Robinson code is self-dual. All these codes are just extended cyclic codes over Z sub 4 . This provides a simple definition for these codes, and explains why their Hamming weight distributions are dual to each other. First- and second-order Reed-Muller codes are also linear codes over Z sub 4 , but Hamming codes in general are not, nor is the Golay code.

Paper available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1993/93-50.ps
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