Title :
The algebraic decoding of the Z4-linear Goethals code
Author :
Helleseth, Tor ; Kumar, Vijay P.
Author_Institution :
Dept. of Inf., Bergen Univ., Norway
fDate :
11/1/1995 12:00:00 AM
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⩾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
Keywords :
Gray codes; decoding; linear codes; Gray map; Z4-linear Goethals code; algebraic decoding; codewords; complete decoding algorithm; covering radius; minimum Lee distance; nonlinear binary code; quaternary Goethals code; Binary codes; Councils; Cryptography; Decoding; Error correction codes; Informatics; Information theory; Meetings; Parity check codes; Polynomials;
Journal_Title :
Information Theory, IEEE Transactions on
