A lower bound on the weight hierarchies of product codes Original Research Article

The weight of a code is the number of coordinate positions where not all codewords are zero. The rth minimum weight dr is the least weight of an r-dimensional subcode. Wei and Yang conjectured a formula for the minimum weights of some product codes, and this conjecture has recently been proved in two different ways. In this self-contained paper, we give a further generalisation, with a new proof which also covers the old results.