Seven infinite classes of relative difference families with variable block sizes are presented explicitly. In particular, a balanced (gv,g,K,1)-DF with $g=\sum_{k\in K}{k^2-k\over2}$ is explicitly given for: (i) K={3,4,5} and every v coprime to 6; (ii) K={3,4,6} or {3,5,6} or {3,4,5,6} and every v coprime to 30. As far as the authors are aware, these difference families can be viewed as the first explicit constructions of infinite classes of optimal variable-weight optical orthogonal codes with more than two weights. It is observed, however, that there are infinitely many values of v for which an optimal (v.W,1,Q) -OOC exists, whatever the set of weights W and the weight distribution sequence Q are.

Relative difference families with variable block sizes and their relatedOOCs / Buratti, Marco; Yueer, Wei; Dianhua, Wu; Pingzhi, Fan; Minquan, Cheng. - In: IEEE TRANSACTIONS ON INFORMATION THEORY. - ISSN 0018-9448. - 57:11(2011), pp. 7489-7497. [10.1109/TIT.2011.2162225]

Relative difference families with variable block sizes and their relatedOOCs

BURATTI, Marco;
2011

Abstract

Seven infinite classes of relative difference families with variable block sizes are presented explicitly. In particular, a balanced (gv,g,K,1)-DF with $g=\sum_{k\in K}{k^2-k\over2}$ is explicitly given for: (i) K={3,4,5} and every v coprime to 6; (ii) K={3,4,6} or {3,5,6} or {3,4,5,6} and every v coprime to 30. As far as the authors are aware, these difference families can be viewed as the first explicit constructions of infinite classes of optimal variable-weight optical orthogonal codes with more than two weights. It is observed, however, that there are infinitely many values of v for which an optimal (v.W,1,Q) -OOC exists, whatever the set of weights W and the weight distribution sequence Q are.
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1654664
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 35
  • ???jsp.display-item.citation.isi??? 35
social impact