Generalized Reed-Muller codes: A new construction of information sets (2401.16911v1)

Abstract: In [2] we show how to construct information sets for Reed-Muller codes only in terms of their basic parameters. In this work we deal with the corresponding problem for q-ary Generalized Reed-Muller codes of first and second order. We see that for first-order codes the result for binary Reed-Muller codes is also valid, while for second-order codes, with q > 2, we have to manage more complex defining sets and we show that we get different information sets. We also present some examples and associated open problems.