Some Bounds on the Size of Codes

Emanuele Bellini (1) , Eleonora Guerrini (2) , Massimiliano Sala (1)

1 UNITN - Università degli Studi di Trento = University of Trento
2 ECO - Exact Computing

We present one upper bound on the size of non-linear codes and its restriction to systematic codes and linear codes. This bound is independent of other known theoretical bounds, e.g. the Griesmer bound, the Johnson bound or the Plotkin bound, and it is an improvement of a bound by Litsyn and Laihonen. Our experiments show that in some cases (the majority of cases for some q) our bounds provide the best value, compared to all other theoretical bounds.

Mots clés: systematic code; linear code; Hamming distance; Upper bound; Non-linear code

Domaines: Théorie de l'information [cs.IT]; Combinatoire [math.CO]

Emanuele Bellini, Eleonora Guerrini, Massimiliano Sala. Some Bounds on the Size of Codes. IEEE Transactions on Information Theory, 2014, 60 (3), pp.1475-1480. ⟨10.1109/TIT.2014.2298234⟩. ⟨lirmm-01282040⟩