Constructions of cyclic quaternary constant-weight codes of weight three and distance four

Lan, Liantao; Chang, Yanxun; Wang, Lidong

doi:10.1007/s10623-017-0379-8

Cited by 3 publications

(13 citation statements)

References 28 publications

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“…The exact values of

C A_{4} false(n, d, 3 false)

are determined for all n and

d \in {1, 2}

d \geq 6

in , and for all n and

d = 4

in . Combining with Lemma and Theorems and , we know that the results on

C A_{4} false(n, d, 3 false)

are determined for all n and d except when

d = 3

and

n \equiv 18 (mod 24)

.…”

Section: Resultsmentioning

confidence: 92%

“…= 30: = {( , − ) ∶ 1 ≤ ≤ 7} ∪ { (8,21), (11,22), (9,18), (10,17), (15,20), (16,19), (12,13)}, = {( , − ) ∶ 1 ≤ ≤ 7, ≠ 2} ∪ { (8,21), (11,22), (19,28), (10,17), (9,14), (15,18), (12,13), (16,20) (16,21), (17,20), (18,19)…”

Section: (Ii)mentioning

confidence: 99%

“…They established some fundamental results of cyclic

{false(n, d, w false)}_{q}

codes from a combinatorial aspect. They presented some general bounds on

C A_{q} false(n, d, w false)

, the maximum size of a cyclic

{false(n, d, w false)}_{q}

code, and determined the the following values: (i)The exact value of

C A_{3} false(n, d, 3 false)

for all d and n in . (ii)The exact value of

C A_{q} false(n, d, 3 false)

for all q , n , and

d \in {1, 2}

d \geq 6

in . (iii)The exact value of

C A_{4} false(n, 4, 3 false)

for all n in . In this paper, we completely determine the value of

C A_{q} false(n, 5, 3 false)

for all q and n . We also give the exact value of

C A_{4} false(n, 3, 3 false)

for any

n ≢ 18 (mod 24)

.…”

Section: Introductionmentioning

confidence: 99%

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Optimal cyclic quaternary constant‐weight codes of weight three

Lan

Chang

2017

J of Combinatorial Designs

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A cyclic false(n,d,wfalse)q code is a cyclic q‐ary code of length n, constant weight w and minimum distance d. Let CAqfalse(n,d,wfalse) denote the largest possible size of a cyclic false(n,d,wfalse)q code. The pure and mixed difference method plays an important role in the determination of upper bound on CAqfalse(n,d,wfalse). By analyzing the distribution of odd mixed and pure differences, an improved upper bound on CA4false(n,3,3false) is obtained for n≡2,4(mod8). A new construction based on special sequences is provided and the exact value of CA4false(n,d,3false) is almost completely determined for all d and n except when d=3 and n≢18(mod24). Our constructions reveal intimate connections between cyclic constant weight codes and special sequences, particularly Skolem‐type sequences.

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“…The exact values of

C A_{4} false(n, d, 3 false)

are determined for all n and

d \in {1, 2}

d \geq 6

in , and for all n and

d = 4

in . Combining with Lemma and Theorems and , we know that the results on

C A_{4} false(n, d, 3 false)

are determined for all n and d except when

d = 3

and

n \equiv 18 (mod 24)

.…”

Section: Resultsmentioning

confidence: 92%

Section: (Ii)mentioning

confidence: 99%

“…They established some fundamental results of cyclic

{false(n, d, w false)}_{q}

codes from a combinatorial aspect. They presented some general bounds on

C A_{q} false(n, d, w false)

, the maximum size of a cyclic

{false(n, d, w false)}_{q}

code, and determined the the following values: (i)The exact value of

C A_{3} false(n, d, 3 false)

for all d and n in . (ii)The exact value of

C A_{q} false(n, d, 3 false)

for all q , n , and

d \in {1, 2}

d \geq 6

in . (iii)The exact value of

C A_{4} false(n, 4, 3 false)

for all n in . In this paper, we completely determine the value of

C A_{q} false(n, 5, 3 false)

for all q and n . We also give the exact value of

C A_{4} false(n, 3, 3 false)

for any

n ≢ 18 (mod 24)

.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal cyclic quaternary constant‐weight codes of weight three

Lan

Chang

2017

J of Combinatorial Designs

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“…Since n is prime, G n = Z * n . Hence, A is a cardioidal starter of order n. The corresponding Skolem sequence is: (1,1,3,4,5,3,18,4,9,5,11,12,13,14,15,16,17,9,19,20,21,11,10,12,18,13,8,14,7,15,6,16,10,17,8,7,6,19,2,20,2,21).…”

Section: Construction Of Cardioidal Startersmentioning

confidence: 99%

“…Here the chord [8,13] violates (d). 3 In particular, property (d) of Theorem 2.1 means that no chord in Figure 1 is horizontal.…”

Section: Introductionmentioning

confidence: 99%

Strong Skolem starters

Ogandzhanyants

Kondratieva

Shalaby

2018

J of Combinatorial Designs

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This paper concerns a class of combinatorial objects called Skolem starters, and more specifically, strong Skolem starters, which are generated by Skolem sequences. In 1991, Shalaby conjectured that any additive group Z n, where n ≡ 1 or 30.3em ( mod0.3em 8 ) ,0.33em n ≥ 11, admits a strong Skolem starter and constructed these starters of all admissible orders 11 ≤ n ≤ 57. Only finitely many strong Skolem starters have been known to date. In this paper, we offer a geometrical interpretation of strong Skolem starters and explicitly construct infinite families of them.

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