Determination of two vectors from the sum

Lindström, Bernt

doi:10.1016/s0021-9800(69)80038-4

Cited by 72 publications

(49 citation statements)

References 3 publications

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“…Next we establish a simple upper bound for s ≤k (C r 2 ), for even k. By Lemma 7.1, the bound for k = 4 follows by results on Sidon sets and the general case is an immediate modification of that argument; for clarity we include the short argument. We point out that by a result of B. Lindström [27], for k = 4, this bound is close to optimal.…”

Section: K (G) For Elementary 2-groupsmentioning

confidence: 60%

Remarks on a generalization of the Davenport constant

Freeze

Schmid

2010

Discrete Mathematics

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A generalization of the Davenport constant is investigated. For a finite abelian group G and a positive integer k, let D k (G) denote the smallest ℓ such that each sequence over G of length at least ℓ has k disjoint non-empty zero-sum subsequences. For general G, expanding on known results, upper and lower bounds on these invariants are investigated and it is proved that the sequence (D k (G)) k∈N is eventually an arithmetic progression with difference exp(G), and several questions arising from this fact are investigated. For elementary 2-groups, D k (G) is investigated in detail; in particular, the exact values are determined for groups of rank four and five (for rank at most three they were already known).

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Section: K (G) For Elementary 2-groupsmentioning

confidence: 60%

Remarks on a generalization of the Davenport constant

Freeze

Schmid

2010

Discrete Mathematics

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“…This ensures they are relative prime. Thus (23) and (24) generalize as S(a 1 (z)) ∩ · · · ∩ S(a L (z)) = {0}, S(a 1 (z)) + · · · + S(a L (z)) = S(a 1 (z) · · · a L (z)).…”

Section: Sequence Construction For Modulo-2 Addition Macmentioning

confidence: 99%

Quickest sequence phase detection

Wang¹,

Shayevitz

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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A phase detection sequence is a length-n cyclic sequence, such that the location of any length-k contiguous subsequence can be determined from a noisy observation of that subsequence. In this paper, we derive bounds on the minimal possible k in the limit of n → ∞, and describe some sequence constructions. We further consider multiple phase detection sequences, where the location of any length-k contiguous subsequence of each sequence can be determined simultaneously from a noisy mixture of those subsequences. We study the optimal trade-offs between the lengths of the sequences, and describe some sequence constructions. We compare these phase detection problems to their natural channel coding counterparts, and show a strict separation between the fundamental limits in the multiple sequence case. Both adversarial and probabilistic noise models are addressed.

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“…Since no two edges cross, by Lemma 4, v i + v j = v k + v ℓ for all distinct pairs {i, j} and {k, ℓ} with i = j and k = ℓ. Sets of binary vectors satisfying Lemma 7 were first studied by Lindström [18,19], and more recently by Cohen et al [4]. Their results can be interpreted as follows, where the lower bound is by Cohen et al [4], and the upper bound follows from (1) and Lemma 5.…”

Section: Hypercube Drawingsmentioning

confidence: 99%