On covering radii and coset weight distributions of extremal binary self-dual codes of length 40

In the present paper we develop a method to determine the coset weight distributions and covering radius of doubly even self-dual extremal binary codes of length 40. The method is algebraic in nature and largely eliminates necessary computations by electronic computers. The method easily applies to longer codes (e.g. self-dual [56,28,12] binary codes) or to non-extremal codes.

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