On silver and golden optical orthogonal codes

Buratti, Marco

doi:10.26493/2590-9770.1236.ce4

Cited by 13 publications

(30 citation statements)

References 22 publications

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“…The necessary conditions for the existence of an APS are established in Lemma 3.1 and we show that these necessary conditions are also sufficient for any APS of order smaller than 300 by using the Kramer‐Mesner method in Theorem 6.6. A silver ratio construction for APS

(p, α, β)

with a prime

p \equiv 7 (\mod 8)

is presented and explored based on Buratti's work in [15]. Recursive constructions are given to produce infinite families of APS

(v, α, β)

s for any

α

and

β

satisfying the necessary conditions.…”

Section: Resultsmentioning

confidence: 99%

“…Usually we write

\sqrt{2}

to represent one of these roots. Buratti introduced silver elements to construct OOCs in [15]. The proof of Theorem 3.1 in [15] uses an APS

(p, 1, \sqrt{2})

implicitly, and so the following lemma has been essentially proved in [15].…”

Section: A Silver Ratio Construction For Apssmentioning

confidence: 99%

“…Strong difference families have been used to construct OOCs in [15,18]. The idea of strong difference families was also implicitly used in [35,40] to construct OOCs.…”

Section: Applications To Optical Orthogonal Codesmentioning

confidence: 99%

“…We remark that in the proof of Theorem 7.1, strong different families are employed implicitly since the first coordinates of elements in

F_{1}

and

F_{2}

form a

(Z_{3}, 4, 4)

‐SDF and a

(Z_{5}, 5, 4)

‐SDF, respectively. We also remark that if the input APS in Theorem 7.1 is an APS

(p, 1, θ - 1)

that is from Lemma 4.1, then the resulting OOCs are those of Theorem 3.1 of [15].…”

Section: Applications To Optical Orthogonal Codesmentioning

confidence: 99%

“…Another motivation comes from an application of PSs and APSs to optical orthogonal codes (OOCs). We note that Buratti's silver ratio construction for OOCs in [15] implies an APS

(p, α, β)

with a prime

p \equiv 7 (\mod 8)

(see Lemma 4.1). This observation makes us believe that the construction of PSs and APSs is a subject worth of deep investigation.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Partitionable sets, almost partitionable sets, and their applications

Chang

Costa

Feng

et al. 2020

J of Combinatorial Designs

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This paper introduces almost partitionable sets (APSs) to generalize the known concept of partitionable sets. These notions provide a unified frame to construct double-struckZ‐cyclic patterned starter whist tournaments and cyclic balanced sampling plans excluding contiguous units. The existences of partitionable sets and APSs are investigated. As an application, a large number of optical orthogonal codes achieving the Johnson bound or the Johnson bound minus one are constructed.

show abstract

(p, α, β)

with a prime

p \equiv 7 (\mod 8)

is presented and explored based on Buratti's work in [15]. Recursive constructions are given to produce infinite families of APS

(v, α, β)

s for any

α

and

β

satisfying the necessary conditions.…”

Section: Resultsmentioning

confidence: 99%

“…Usually we write

\sqrt{2}

to represent one of these roots. Buratti introduced silver elements to construct OOCs in [15]. The proof of Theorem 3.1 in [15] uses an APS

(p, 1, \sqrt{2})

implicitly, and so the following lemma has been essentially proved in [15].…”

Section: A Silver Ratio Construction For Apssmentioning

confidence: 99%

“…Strong difference families have been used to construct OOCs in [15,18]. The idea of strong difference families was also implicitly used in [35,40] to construct OOCs.…”

Section: Applications To Optical Orthogonal Codesmentioning

confidence: 99%

“…We remark that in the proof of Theorem 7.1, strong different families are employed implicitly since the first coordinates of elements in

F_{1}

and

F_{2}

form a

(Z_{3}, 4, 4)

‐SDF and a

(Z_{5}, 5, 4)

‐SDF, respectively. We also remark that if the input APS in Theorem 7.1 is an APS

(p, 1, θ - 1)

that is from Lemma 4.1, then the resulting OOCs are those of Theorem 3.1 of [15].…”

Section: Applications To Optical Orthogonal Codesmentioning

confidence: 99%

“…Another motivation comes from an application of PSs and APSs to optical orthogonal codes (OOCs). We note that Buratti's silver ratio construction for OOCs in [15] implies an APS