Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Optical orthogonal signature pattern codes (OOSPCs) play an important role in a novel type of optical code-division multiple-access network for 2-dimensional image transmission. There is a one-to-one correspondence beten an \((m, n, w, \lambda )\)-OOSPC and a \((\lambda +1)\)-(mn, w, 1) packing design admitting an automorphism group isomorphic to \(\mathbb {Z}_m\times \mathbb {Z}_n\). In 2010, Sawa gave a construction of an (m, n, 4, 2)-OOSPC from a one-factor of Kohler graph of \(\mathbb {Z}_m\times \mathbb {Z}_n\) which contains a unique element of order 2. ,  study the existence of one-factor of Kohler graph of \(\mathbb {Z}_m\times \mathbb {Z}_n\) having three elements of order 2. It is proved that there is a one-factor in the Kohler graph of \(\mathbb {Z}_{2^{\epsilon }p}\times \mathbb {Z}_{2^{\epsilon '}}\) relative to the Sylow 2-subgroup if there is an S-cyclic Steiner quadruple system of order 2p, where \(p\equiv 5\pmod {12}\) is a prime and \(1\le \epsilon ,\epsilon '\le 2\). Using this one-factor,  construct a strictly \(\mathbb {Z}_{2^{\epsilon }p}\times \mathbb {Z}_{2^{\epsilon '}}\)-invariant regular \(G^*(p,2^{\epsilon +\epsilon '},4,3)\) relative to the Sylow 2-subgroup. By using the known S-cyclic SQS(2p) and a recursive construction for strictly \(\mathbb {Z}_{m}\times \mathbb {Z}_{n}\)-invariant regular G-designs,  construct more strictly \(\mathbb {Z}_{m}\times \mathbb {Z}_{n}\)-invariant 3-(mn, 4, 1) packing designs. Consequently, there is an optimal \((2^{\epsilon }m,2^{\epsilon '}n,4,2)\)-OOSPC for any \(\epsilon ,\epsilon '\in \{0,1,2\}\) with \(\epsilon +\epsilon '>0\) and an optimal (6m, 6n, 4, 2)-OOSPC where m, n are odd integers whose all prime divisors from the set \(\{p\equiv 5\pmod {12}:p\) is a prime, \(p<\)1,500,000}.
['Jingyuan Chen', 'Lijun Ji', 'Yun Li']
I am writing a research paper on a idea New optical orthogonal signature pattern codes with maximum collision parameter 2 and weight 4
[{"from": "human", "value": "I am writing a research paper on a idea New optical orthogonal signature pattern codes with maximum collision parameter 2 and weight 4"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Optical orthogonal signature pattern codes (OOSPCs) play an important role in a novel type of optical code-division multiple-access network for 2-dimensional image transmission. There is a one-to-one correspondence beten an \\((m, n, w, \\lambda )\\)-OOSPC and a \\((\\lambda +1)\\)-(mn, w, 1) packing design admitting an automorphism group isomorphic to \\(\\mathbb {Z}_m\\times \\mathbb {Z}_n\\). In 2010, Sawa gave a construction of an (m, n, 4, 2)-OOSPC from a one-factor of Kohler graph of \\(\\mathbb {Z}_m\\times \\mathbb {Z}_n\\) which contains a unique element of order 2. ,  study the existence of one-factor of Kohler graph of \\(\\mathbb {Z}_m\\times \\mathbb {Z}_n\\) having three elements of order 2. It is proved that there is a one-factor in the Kohler graph of \\(\\mathbb {Z}_{2^{\\epsilon }p}\\times \\mathbb {Z}_{2^{\\epsilon '}}\\) relative to the Sylow 2-subgroup if there is an S-cyclic Steiner quadruple system of order 2p, where \\(p\\equiv 5\\pmod {12}\\) is a prime and \\(1\\le \\epsilon ,\\epsilon '\\le 2\\). Using this one-factor,  construct a strictly \\(\\mathbb {Z}_{2^{\\epsilon }p}\\times \\mathbb {Z}_{2^{\\epsilon '}}\\)-invariant regular \\(G^*(p,2^{\\epsilon +\\epsilon '},4,3)\\) relative to the Sylow 2-subgroup. By using the known S-cyclic SQS(2p) and a recursive construction for strictly \\(\\mathbb {Z}_{m}\\times \\mathbb {Z}_{n}\\)-invariant regular G-designs,  construct more strictly \\(\\mathbb {Z}_{m}\\times \\mathbb {Z}_{n}\\)-invariant 3-(mn, 4, 1) packing designs. Consequently, there is an optimal \\((2^{\\epsilon }m,2^{\\epsilon '}n,4,2)\\)-OOSPC for any \\(\\epsilon ,\\epsilon '\\in \\{0,1,2\\}\\) with \\(\\epsilon +\\epsilon '>0\\) and an optimal (6m, 6n, 4, 2)-OOSPC where m, n are odd integers whose all prime divisors from the set \\(\\{p\\equiv 5\\pmod {12}:p\\) is a prime, \\(p<\\)1,500,000}."}]