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Z4-linear Hadamard and extended perfect codes

โœ Scribed by D.S. Krotov

Book ID
104444185
Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
376 KB
Volume
6
Category
Article
ISSN
1571-0653

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โœฆ Synopsis

If N = 2 k 16 then there exist exactly b(k 1)=2c pairwise nonequivalent Z 4linear Hadamard (N 2N N = 2)-codes and b(k + 1 ) =2c pairwise nonequivalent Z 4linear extended perfect (N 2 N =2N 4)-codes. Recurrent construction of Z 4 -linear Hadamard codes is given.

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โœ M. van Eupen; Vladimir D. Tonchev ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 284 KB

Linear codes over GF(5) are utilized for the construction of a reversible abelian Hadamard difference set in Z 2 \_Z 2 \_Z 4 5 . This is the first example of an abelian Hadamard difference set in a group of order divisible by a prime p#1 (mod 4). Applying the Turyn composition theorem, one obtains a