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

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

29 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
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

Bibliographical note

Funding Information:
* Research supported in part by Allon Fellowship and by a Bat Sheva de Rothschild Grant. ’ Research supported in part by Air Force Office of Scientific Research Grant AFOSR-0271.

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title = "Additive bases of vector spaces over prime fields",

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.",

author = "N. Alon and N. Linial and R. Meshulam",

note = "Funding Information: * Research supported in part by Allon Fellowship and by a Bat Sheva de Rothschild Grant. {\textquoteright} Research supported in part by Air Force Office of Scientific Research Grant AFOSR-0271.",

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AU - Linial, N.

AU - Meshulam, R.

N1 - Funding Information: * Research supported in part by Allon Fellowship and by a Bat Sheva de Rothschild Grant. ’ Research supported in part by Air Force Office of Scientific Research Grant AFOSR-0271.

PY - 1991/7

Y1 - 1991/7

N2 - 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.

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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Additive bases of vector spaces over prime fields

Abstract

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