Binary linear codes with two or three weights from niho exponents

We characterize the connection between p-ary linear codes and Ramanujan Cayley graphs. We explicitly determine an equivalence between tweight 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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“…In the past two years, constructing linear codes from this approach and studying the weight distributions of these linear codes have attracted extensively attention, see e.g. [12,26,37,11,20].…”

Section: Let Tr Mmentioning

confidence: 99%

Two classes of near-optimal codebooks with respect to the Welch bound

Luo¹,

Cao²

2021

Advances in Mathematics of Communications

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An (N, K) codebook C is a collection of N unit norm vectors in a K-dimensional vectors space. In applications of codebooks such as CDMA, those vectors in a codebook should have a small maximum magnitude of inner products between any pair of distinct code vectors. In this paper, we propose two constructions of codebooks based on p-ary linear codes and on a hybrid character sum of a special kind of functions, respectively. With these constructions, two classes of codebooks asymptotically meeting the Welch bound are presented.

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Binary linear codes with two or three weights from niho exponents

Cited by 45 publications

References 23 publications

Two-weight and three-weight linear codes based on Weil sums

Two-weight and three-weight linear codes based on Weil sums

Connection of <inline-formula><tex-math id="M1">$ p $</tex-math></inline-formula>-ary <inline-formula><tex-math id="M2">$ t $</tex-math></inline-formula>-weight linear codes to Ramanujan Cayley graphs with <inline-formula><tex-math id="M3">$ t+1 $</tex-math></inline-formula> eigenvalues

Two classes of near-optimal codebooks with respect to the Welch bound

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