Additive bases of vector spaces over prime fields

N. Alon; N. Linial; R. Meshulam

doi:10.1016/0097-3165(91)90045-I

Additive bases of vector spaces over prime fields

N. Alon, N. Linial, R. Meshulam

Research output: Contribution to journal › Article

25 Scopus citations

Abstract

It is shown that for any t > c_plog n linear bases B₁, ..., B_t of Z_pⁿ their union (with repetitions) ∪_{i = 1}^t B_i forms an additive basis of Z_pⁿ; i.e., for any x ε{lunate} Z_pⁿ there exist A₁ ⊃ B₁, ..., A_t ⊃ B_t such that x = Σ_{i = 1}^t Σ_{y ε{lunate} A_i} y.

Original language	English (US)
Pages (from-to)	203-210
Number of pages	8
Journal	Journal of Combinatorial Theory, Series A
Volume	57
Issue number	2
DOIs	https://doi.org/10.1016/0097-3165(91)90045-I
State	Published - Jul 1991
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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Alon, N., Linial, N., & Meshulam, R. (1991). Additive bases of vector spaces over prime fields. Journal of Combinatorial Theory, Series A, 57(2), 203-210. https://doi.org/10.1016/0097-3165(91)90045-I

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abstract = "It is shown that for any t > cplog n linear bases B1, ..., Bt of Zpn their union (with repetitions) ∪i = 1t Bi forms an additive basis of Zpn; i.e., for any x ε{lunate} Zpn there exist A1 ⊃ B1, ..., At ⊃ Bt such that x = Σi = 1t Σy ε{lunate} Ai y.",

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AB - It is shown that for any t > cplog n linear bases B1, ..., Bt of Zpn their union (with repetitions) ∪i = 1t Bi forms an additive basis of Zpn; i.e., for any x ε{lunate} Zpn there exist A1 ⊃ B1, ..., At ⊃ Bt such that x = Σi = 1t Σy ε{lunate} Ai y.

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