Title :
A Group Ring Construction of the Extended Binary Golay Code
Author :
McLoughlin, Ian ; Hurley, Ted
Author_Institution :
Nat. Univ. of Ireland, Galway
Abstract :
We give a new construction of the extended binary Golay code. The code is constructed as a zero divisor code over the dihedral group of twenty-four elements, D 24. The construction is algebraic, much like the construction of the (23,12,7) binary Golay code from a polynomial.
Keywords :
Golay codes; block codes; cyclic codes; group theory; extended binary Golay code; group ring construction; Binary codes; Block codes; Councils; Decoding; Linear algebra; Mathematics; Terminology; Vectors; Block codes; Golay codes; dual codes; group theory; rings (algebraic);
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2008.928260
