On constructions for optimal two-dimensional optical orthogonal codes

Wang, Jianmin; Shan, Xiuling; Yin, Jianxing

doi:10.1007/s10623-009-9308-9

Cited by 21 publications

(21 citation statements)

References 45 publications

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“…Finally, we make a remark. It is known in that an optimal 2–D

(n \times m, 3, 1)

‐OOC with

J (n \times m, 3, 1)

codewords exists for any positive integer n and odd integer m except for

m = 1

and

n \equiv 5 (\mod 6)

, where in the latter case, an optimal 2‐D

(n \times 1, 3, 1)

‐OOC only has

J (n \times 1, 3, 1) - 1

codewords. For the case of m even, it seems that the problem is still open.…”

Section: Applicationsmentioning

confidence: 99%

Semi-cyclic Holey Group Divisible Designs and Applications to Sampling Designs and Optical Orthogonal Codes

2014

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Abstract:We consider the existence problem for a semi-cyclic holey group divisible design of type (n, m t ) with block size 3, which is denoted by a 3-SCHGDD of type (n, m t ). When t is odd and n = 8 or t is doubly even and t = 8, the existence problem is completely solved; when t is singly even, many infinite families are obtained. Applications of our results to twodimensional balanced sampling plans and optimal two-dimensional optical orthogonal codes are also discussed.

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“…Finally, we make a remark. It is known in that an optimal 2–D

(n \times m, 3, 1)

‐OOC with

J (n \times m, 3, 1)

codewords exists for any positive integer n and odd integer m except for

m = 1

and

n \equiv 5 (\mod 6)

, where in the latter case, an optimal 2‐D

(n \times 1, 3, 1)

‐OOC only has

J (n \times 1, 3, 1) - 1

codewords. For the case of m even, it seems that the problem is still open.…”

Section: Applicationsmentioning

confidence: 99%

Semi-cyclic Holey Group Divisible Designs and Applications to Sampling Designs and Optical Orthogonal Codes

2014

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“…Usually a k-HGDD obtained by this manner is said to be a semi-cyclic k-HGDD and denoted by a k-SCHGDD. k-SCHGDDs were first introduced in [30] to construct optimal two-dimensional optical orthogonal codes.…”

Section: For Details)mentioning

confidence: 99%

Semi-cyclic holey group divisible designs with block size three

Feng

Wang

Chang

2013

Des. Codes Cryptogr.

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In this paper we discuss the existence problem for a semi-cyclic holey group divisible design of type (n, m t ) with block size 3, which is denoted by a 3-SCHGDD of type (n, m t ). When n = 3, a 3-SCHGDD of type (3, m t ) is equivalent to a (3, mt; m)-cyclic holey difference matrix, denoted by a (3, mt; m)-CHDM.It is shown that there is a (3, mt; m)-CHDM if and only if (t − 1)m ≡ 0 (mod 2) and t ≥ 3 with the exception of m ≡ 0 (mod 2) and t = 3. When n ≥ 4, the case of t odd is considered. It is established that if t ≡ 1 (mod 2) and n ≥ 4, then there exists a 3-SCHGDD of type (n, m t ) if and only if t ≥ 3 and (t − 1)n(n − 1)m ≡ 0 (mod 6) with some possible exceptions of n = 6 and 8. The main results in this paper have been used to construct optimal two-dimensional optical orthogonal codes with weight 3 and different auto-and cross-correlation constraints by the authors recently.

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“…When

λ_{a} = λ_{c} = λ

, much work has been done by many authors to determine the exact value of

Φ (n \times m, k, λ, λ)

. The reader may refer to for more information.…”

Section: Introductionmentioning

confidence: 99%

Optimal Two‐Dimensional Optical Orthogonal Codes with the Best Cross‐Correlation Constraint

Feng

Wang

et al. 2016

J of Combinatorial Designs

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The study of optical orthogonal codes has been motivated by an application in an optical code‐division multiple access system. From a practical point of view, compared to one‐dimensional optical orthogonal codes, two‐dimensional optical orthogonal codes tend to require smaller code length. On the other hand, in some circumstances only with good cross‐correlation one can deal with both synchronization and user identification. These motivate the study of two‐dimensional optical orthogonal codes with better cross‐correlation than auto‐correlation. This paper focuses on optimal two‐dimensional optical orthogonal codes with the auto‐correlation λa and the best cross‐correlation 1. By examining the structures of w‐cyclic group divisible designs and semi‐cyclic incomplete holey group divisible designs, we present new combinatorial constructions for two‐dimensional (n×m,k,λa,1)‐optical orthogonal codes. When k=3 and λa=2, the exact number of codewords of an optimal two‐dimensional (n×m,3,2,1)‐optical orthogonal code is determined for any positive integers n and m≡2(mod4).

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On constructions for optimal two-dimensional optical orthogonal codes

Cited by 21 publications

References 45 publications

Semi-cyclic Holey Group Divisible Designs and Applications to Sampling Designs and Optical Orthogonal Codes

Semi-cyclic Holey Group Divisible Designs and Applications to Sampling Designs and Optical Orthogonal Codes

Semi-cyclic holey group divisible designs with block size three

Optimal Two‐Dimensional Optical Orthogonal Codes with the Best Cross‐Correlation Constraint

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