Divisors of codes of Reed-Muller type (Q1332412)

Let \(F\) denote the finite field \(GF(q)\) where \(q\) is a power of the prime \(p\). The exponent of a linear code over \(F\) is the exponent of the highest power of \(p\) that divides all the codeword weights. It is shown how to compute the exponents of codes in a class that includes radical powers in group algebras of arbitrary \(p\)-groups. The computation involves the solution of the combinatorial bin-packing problem, known to be NP-complete. For some groups, including Abelian groups, it is shown that certain standard algorithms for this problem produce optimal solutions and yield the exact exponent.