Numerical experiments related to the covering radius of some first order Reed-Muller codes
We have done some numerical experiments to find large coset leaders for the first order Reed-Muller codes RM(m) of length 2m for odd m,m ≥ 9, by using some matrix groups acting on the field GF(2m) viewed as a GF(2)-vector space. The coset leaders so obtained are characteristic functions of subsets of GF(2m) that are union of orbits under the considered group and often have interesting combinatorial properties generalizing difference sets.
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