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Double-weight optical orthogonal codes are variable-weight optical orthogonal codes (OOCs), which have been widely applied in optical networks and systems. Some works have been devoted to optimal  n , W , 1 , Q -OOCs with  max w : w ∈ W ≤ 6 . So far, there is no explicit construction of optimal  n , W , 1 , Q -OOCs with  W = 5,7 . It is known that heavier-weight codewords have better code performance than lighter-weight codewords. So, in this paper, we use cyclic packing to construct two infinite classes of optimal OOCs with weights set  5,7 explicitly, for any prime  p ≡ 3 mod 4 and  p ≥ 7 . In addition, for  1 ≤ t &lt; p − 1 / 2 , by breaking  t blocks of size 7 into 3 of  31 p , 5,7 , 1 , 1 / 2 , 1 / 2 -OOCs and  41 p , 5,7 , 1 , 2 / 3 , 1 / 3 -OOCs, we obtain new infinite classes of optimal  31 p , 3,5,7 , 1 , 7 t / p − 1 + 6 t , p − 1 / 2 p − 1 + 6 t , p − 1 − 2 t / 2 p − 1 + 6 t -OOCs and  41 p , 3,5,7 , 1 , 14 t / 3 p − 1 + 4 t , 2 p − 1 / 3 p − 1 + 4 t , p − 1 − 2 t / 3 p − 1 + 4 t -OOCs, respectively.

mathematical problems in engineering

Constructions of Optimal Optical Orthogonal Codes with Weights Set <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mfenced open="{" close="}" separators="|"> <mrow> <mn>5,7</mn> </mrow> </mfenced> </math> via Cyclic Packing

Constructions of Optimal Optical Orthogonal Codes with Weights Set 5,7 via Cyclic Packing

Constructions of Optimal Optical Orthogonal Codes with Weights Set $\{5,7\}$ via Cyclic Packing