2024/03/07 by Kurz, Sascha
#004 #510 #Divisible codes #Galois geometry #linear codes
paper · doi:10.15495/epub_ubt_00007502
A linear code C over GF(q) is called Δ-divisible if the Hamming weights wt(c) of all codewords c in C are divisible by Δ. The possible effective lengths of qr-divisible codes have been completely characterized for each prime power q and each non-negative integer r. The study of Δ divisible codes was initiated by Harold Ward. If c divides Δ but is coprime to q, then each Δ-divisible code C over GF(q) is the c-fold repetition of a Δ/c-divisible code. Here we determine the possible effective lengths of pr-divisible codes over finite fields of characteristic p, where r is an integer but pr is not a power of the field size, i.e., the missing cases.