The algebraic decoding of the Z4 linear Goethals code

Helleseth, T. ; Kumar, P. V. (1995) The algebraic decoding of the Z4 linear Goethals code IEEE Transactions on Information Theory, 41 (6). pp. 2040-2048. ISSN 0018-9448

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Official URL: http://ieeexplore.ieee.org/document/476333/

Related URL: http://dx.doi.org/10.1109/18.476333

Abstract

The quaternary Goethals code is a Z4-linear code of length 2m which has 2(2m+1)(-3m-2) codewords and minimum Lee distance 8 for any odd integer m/spl ges/3. The Gray map of this code is known to be a nonlinear binary (2m+1, 2(2m+1)(-3m-2), 8) code. The covering radius of the Z4-linear Goethals code is 6 and we present a complete decoding algorithm for the code.

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