CONNECTION OF p-ARY t-WEIGHT LINEAR CODES TO RAMANUJAN CAYLEY GRAPHS WITH t + 1 EIGENVALUES

Jong Yoon Hyun; Yoonjin Lee; Yansheng Wu

doi:10.3934/amc.2020133

CONNECTION OF p-ARY t-WEIGHT LINEAR CODES TO RAMANUJAN CAYLEY GRAPHS WITH t + 1 EIGENVALUES

Jong Yoon Hyun, Yoonjin Lee, Yansheng Wu

Department of Mathematics

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

Abstract

We characterize the connection between p-ary linear codes and Ramanujan Cayley graphs. We explicitly determine an equivalence between t-weight linear codes over the finite field F_p and Ramanujan Cayley graphs with t + 1 eigenvalues. In particular, we get an explicit criterion on the equivalence between two-weight linear codes and Ramanujan strongly regular graphs with explicit parameters. Using this characterization, we construct several families of Ramanujan Cayley graphs with two or three eigenvalues from known linear codes with two or three weights, respectively.

Original language	English
Pages (from-to)	367-380
Number of pages	14
Journal	Advances in Mathematics of Communications
Volume	17
Issue number	2
DOIs	https://doi.org/10.3934/amc.2020133
State	Published - Apr 2023

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© 2023, American Institute of Mathematical Sciences. All rights reserved.

Keywords

Cayley graph
Ramanujan graph
linear code
strongly regular graph
two-weight code
weakly regular bent function

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10.3934/amc.2020133

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N2 - We characterize the connection between p-ary linear codes and Ramanujan Cayley graphs. We explicitly determine an equivalence between t-weight linear codes over the finite field Fp and Ramanujan Cayley graphs with t + 1 eigenvalues. In particular, we get an explicit criterion on the equivalence between two-weight linear codes and Ramanujan strongly regular graphs with explicit parameters. Using this characterization, we construct several families of Ramanujan Cayley graphs with two or three eigenvalues from known linear codes with two or three weights, respectively.

AB - We characterize the connection between p-ary linear codes and Ramanujan Cayley graphs. We explicitly determine an equivalence between t-weight linear codes over the finite field Fp and Ramanujan Cayley graphs with t + 1 eigenvalues. In particular, we get an explicit criterion on the equivalence between two-weight linear codes and Ramanujan strongly regular graphs with explicit parameters. Using this characterization, we construct several families of Ramanujan Cayley graphs with two or three eigenvalues from known linear codes with two or three weights, respectively.

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KW - Ramanujan graph

KW - linear code

KW - strongly regular graph

KW - two-weight code

KW - weakly regular bent function

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CONNECTION OF p-ARY t-WEIGHT LINEAR CODES TO RAMANUJAN CAYLEY GRAPHS WITH t + 1 EIGENVALUES

Abstract

Bibliographical note

Keywords

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