438 and references

On covering radii and coset weight distributions of extremal binary self-dual codes of length 40. (English summary) Combinatorics and optimization (Okinawa, 1996). Theoret. Comput. Sci. 235 (2000), no. 2, 283–308. Let C be a self-dual binary code. The author shows that the weight enumerator of any coset of C can be expressed in terms of a Jacobi polynomial. By understanding the invariance properties of Jacobi polynomials, the author develops a method to calculate the coset weight distributions, and hence the covering radii, of extremal doubly-even self-dual binary codes. Explicit results are given for two [40, 20, 8] codes whose covering radii turn out to equal 8. {For the entire collection see MR1756120 (2000m:05004)