ترغب بنشر مسار تعليمي؟ اضغط هنا

Constructions and necessities of some permutation polynomials

173   0   0.0 ( 0 )
 نشر من قبل Xiaogang Liu
 تاريخ النشر 2019
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English
 تأليف Xiaogang Liu




اسأل ChatGPT حول البحث

Permutation polynomials over finite fields have important applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, etc. In this paper, we construct several new classes of permutation polynomials, and the necessities of some permutation polynomials are studied.



قيم البحث

اقرأ أيضاً

74 - Xiaogang Liu 2019
For the finite field $mathbb{F}_{2^{3m}}$, permutation polynomials of the form $(x^{2^m}+x+delta)^{s}+cx$ are studied. Necessary and sufficient conditions are given for the polynomials to be permutation polynomials. For this, the structures and properties of the field elements are analyzed.
Four recursive constructions of permutation polynomials over $gf(q^2)$ with those over $gf(q)$ are developed and applied to a few famous classes of permutation polynomials. They produce infinitely many new permutation polynomials over $gf(q^{2^ell})$ for any positive integer $ell$ with any given permutation polynomial over $gf(q)$. A generic construction of permutation polynomials over $gf(2^{2m})$ with o-polynomials over $gf(2^m)$ is also presented, and a number of new classes of permutation polynomials over $gf(2^{2m})$ are obtained.
259 - Xiaogang Liu 2019
Let $mathbb{F}_q$ denote the finite fields with $q$ elements. The permutation behavior of several classes of infinite families of permutation polynomials over finite fields have been studied in recent years. In this paper, we continue with their stud ies, and get some further results about the permutation properties of the permutation polynomials. Also, some new classes of permutation polynomials are constructed. For these, we alter the coefficients, exponents or the underlying fields, etc.
256 - Zilong Wang , Guang Gong 2020
In this paper, a recent method to construct complementary sequence sets and complete complementary codes by Hadamard matrices is deeply studied. By taking the algebraic structure of Hadamard matrices into consideration, our main result determine the so-called $delta$-linear terms and $delta$-quadratic terms. As a first consequence, a powerful theory linking Golay complementary sets of $p$-ary ($p$ prime) sequences and the generalized Reed-Muller codes by Kasami et al. is developed. These codes enjoy good error-correcting capability, tightly controlled PMEPR, and significantly extend the range of coding options for applications of OFDM using $p^n$ subcarriers. As another consequence, we make a previously unrecognized connection between the sequences in CSSs and CCCs and the sequence with 2-level autocorrelation, trace function and permutation polynomial (PP) over the finite fields.
94 - Weijun Fang , Fang-Wei Fu 2018
It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes of q-ary quantum MDS codes by using generalized Reed-Solomon (GRS) codes and Hermitian construc tion. The minimum distances of our quantum MDS codes can be larger than q/2+1 Three of these six classes of quantum MDS codes have longer lengths than the ones constructed in [1] and [2], hence some of their results can be easily derived from ours via the propagation rule. Moreover, some known quantum MDS codes of specific lengths can be seen as special cases of ours and the minimum distances of some known quantum MDS codes are also improved as well.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا