arXiv subjects

Saban Alaca

Publications and source records attributed to Saban Alaca.

4 recordsLinked to original sources

arXiv2022

Low-Density Spreading Design Based on an Algebraic Scheme for NOMA Systems

NOMA) technique based on an algebraic design is studied. We propose an improved low-density spreading (LDS) sequence design based on projective geometry. In terms of its bit error rate (BER) performance, our proposed improved LDS code set outperforms the existing LDS designs over the frequency nonselective Rayleigh fading and additive white Gaussian noise (AWGN) channels. We demonstrated that achieving the best BER depends on the minimum distance.

cs.IT↗

arXiv2018

Shift-Inequivalent Decimations of the Sidelnikov-Lempel-Cohn-Eastman Sequences

We consider the problem of finding maximal sets of shift-inequivalent decimations of Sidelnikov-Lempel-Cohn-Eastman (SLCE) sequences (as well as the equivalent problem of determining the multiplier groups of the almost difference sets associated with these sequences). We derive a numerical necessary condition for a residue to be a multiplier of an SLCE almost difference set. Using our necessary condition, we show that if $p$ is an odd prime and $S$ is an SLCE almost difference set over $\mathbb{F}_p,$ then the multiplier group of $S$ is trivial. Consequently, for each odd prime $p,$ we obtain a family of $ϕ(p-1)$ shift-inequivalent balanced periodic sequences (where $ϕ$ is the Euler-Totient function) each having period $p-1$ and nearly perfect autocorrelation.

math.CO↗

arXiv2016

Eta quotients, Eisenstein series and Elliptic Curves

We express all the newforms of weight $2$ and levels $30$, $33$, $35$, $38$, $40$, $42$, $44$, $45$ as linear combinations of eta quotients and Eisenstein series, and list their corresponding strong Weil curves. Let $p$ denote a prime and $E (\zz_p)$ denote the the group of algebraic points of an elliptic curve $E$ over $\zz_p$. We give a generating function for the order of $E (\zz_p)$ for certain strong Weil curves in terms of eta quotients and Eisenstein series. We then use our generating functions to deduce congruence relations for the order of $E (\zz_p)$ for those strong Weil curves.

math.NT↗

arXiv2016

A family of Eta Quotients and an Extension of the Ramanujan-Mordell Theorem

Let $k\geq 2$ be an integer and $j$ an integer satisfying $1\leq j \leq 4k-5$. We define a family $\{ C_{j,k}(z) \}_{1\leq j \leq 4k-5} $ of eta quotients, and prove that this family constitute a basis for the space $S_{2k} (Γ_0 (12))$ of cusp forms of weight $2k$ and level $12$. We then use this basis together with certain properties of modular forms at their cusps to prove an extension of the Ramanujan-Mordell formula.

math.NT↗