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

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