ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

3. Number Theory and Arithmetic Algebraic Geometry

1991 MS Classification: 11T, 94B Ling, San, National University of Singapore, Singapore Group algebras and codes Using the group algebra of an abelian group and a splitting of the group, we construct a class of [n, (n + 1)/2] codes such that the minimum distance outside of a certain subcode is ≥ \sqrt{n}, a well-known bound for quadratic residue codes. The construction yields quadratic residue codes, generalised quadratic residue codes, duadic codes and Q-codes as special cases. We show that the split codes so constructed properly contain the above classes of codes and that new codes arise even over 𝔽_{2}. This is joint work with C. S. Ding and D. R. Kohel.