2026/07/16 by Tuvi Etzion
Computer Science · Mathematics · #cs.IT #math.IT
An (n,R)q-covering sequence is a cyclic sequence, over the finite field \Fq, whose consecutive n-tuples form a code of length n and covering radius R. An (n,m,R)q-covering-sequences code is a set of cyclic sequences of length m, over \Fq, whose consecutive n-tuples form a code of length n and covering radius R. These codes are the best building blocks for (n,R)q-covering sequences. We show, for small radii, how cyclic codes and constacyclic codes with small covering radius, can be used to construct such sequences of short length and such codes with a relatively small number of sequences and a total number of codewords in the associated covering code. Sequences with small radius whose length approaches asymptotically to optimality are constructed, especially for an alphabet of prime power size large enough. With the same construction, interesting codes are also constructed for larger radii.