On the majority decodable distance of codes in filtrations of characteristic \(p>0\) (Q1312351)

In this article, the ideals contained in a filtration of the augmentation ideal of the group algebra \(KG\) of a finite \(p\)-group over a finite field \(K\) of characteristic \(p\) are considered as linear codes. For each such code a lower bound on the number of errors can be corrected by majority logic is given. It turns out that at least every \((p-1)\)-th code occuring in such a filtration is completely majority logic decodable; in particular, every such binary code is completely majority logic decodable. Moreover, for generalized Reed-Muller codes over the primes lower bounds on the number of errors correctable by majority logic are presented.