On Code Distances of Some Classes of $(p,p)$-Codes

The author derives an exact formula for the code distance of the direct sum of three minimal ideals of the group algebra of group $G=(a)\times(b)$, $a^p=b^p=1$, over a field of characteristic 2 for primes $p$ of the form $4t-1$. The proposed method of proof yields an efficient way of calculating the elements of the code of minimal nonzero weight.