Nearly optimal codebooks based on generalized Jacobi sums

Six constructions of asymptotically optimal codebooks via the character sums

In this paper, using additive characters of finite field, we find a codebook which is equivalent to the measurement matrix in [20]. The advantage of our construction is that it can be generalized naturally to construct the other five classes of codebooks using additive and multiplicative characters of finite field. We determine the maximal cross-correlation amplitude of these codebooks by the properties of characters and character sums. We prove that all the codebooks we constructed are asymptotically optimal with respect to the Welch bound. The parameters of these codebooks are new.

The Jacobi sums over Galois rings of arbitrary characters and their applications in constructing asymptotically optimal codebooks

Codebooks with small maximum cross-correlation amplitudes are used to distinguish the signals from different users in CDMA communication systems. In this paper, we first study the Jacobi sums over Galois rings of arbitrary characteristics and completely determine their absolute values, which extends the work in [34], where the Jacobi sums over Galois rings with characteristics of a square of a prime number were discussed. Then, the deterministic construction of codebooks based on the Jacobi sums over Galois rings of arbitrary characteristics is presented, which produces asymptotically optimal …

New constructions of asymptotically optimal codebooks via character sums over a local ring

In this paper, we present explicit description on the additive characters, multiplicative characters and Gauss sums over a local ring. As an application, based on the additive characters and multiplicative characters satisfying certain conditions, two new constructions of complex codebooks over a local ring are introduced. With these two constructions, we obtain two families of codebooks achieving asymptotically optimal with respect to the Welch bound. It's worth mentioning that the codebooks constructed in this paper have new parameters.

源自向量化对偶Bent函数的混合特征和及具有小字母表尺寸的渐近最优复数码本

Hybrid Character Sums From Vectorial Dual-Bent Functions and Asymptotically Optimal Complex Codebooks With Small Alphabet Sizes

本文研究了源自向量化对偶Bent函数的混合特征和，确定了其在特定条件下的复模长或显式值，并据此构造了三族具有极小字母表尺寸和两值或三值互相关幅值的渐近最优复数码本。

On the Jacobi sums over Galois rings

In this paper, we study the Jacobi sums over Galois rings of arbitrary characteristics and completely determine their absolute values, which extends the work in \cite{feng1}, where the Jacobi sums over Galois rings with characteristics a square of a prime number were discussed.

Jacobi Sums and Correlations of Sidelnikov Sequences

We consider the problem of determining the cross-correlation values of the sequences in the families comprised of constant multiples of $M$-ary Sidelnikov sequences over $\mathbb{F}_q$, where $q$ is a power of an odd prime $p$. We show that the cross-correlation values of pairs of sequences from such a family can be expressed in terms of certain Jacobi sums. This insight facilitates the computation of the cross-correlation values of these sequence pairs so long as $ϕ(M)^{ϕ(M)} \leq q.$ We are also able to use our Jacobi sum expression to deduce explicit formulae for the cross-correlation distr…