Abstract
In this paper, we discuss about restrictions of optical orthogonal codes (OOC) to subgroups and obtain variable weight OOCs in which the weight of each codeword is lower and upper bounded in relation to a character sum over finite fields. We show that the following three new series of optimal or asymptotically optimal constant weight OOCs are included in those variable weight ones: (i) an optimal ( q 2 − 1 e , ⌈ q − ( e − 1 ) q e ⌉ , 1 ) -OOC with e codewords; (ii) an optimal ( q 2 + q + 1 e , ⌈ q + 1 − ( e − 1 ) q e ⌉ , 1 ) -OOC with e codewords; and (iii) an asymptotically optimal ( q 2 − 1 e , ⌈ q − 3 ( e − 1 ) q e ⌉ , 2 ) -OOC with e ( q − 1 ) codewords.
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