On divisibility of exponential sums of polynomials of special type over fields of characteristic 2

نویسندگان

  • Leonid A. Bassalygo
  • Victor Zinoviev
چکیده

We study divisibility by eight of exponential sums of several classes of functions over finite fields of characteristic two. For the binary classical Kloosterman sums K(a) over such fields we give a simple recurrent algorithm for finding the largest k, such that 2 divides the Kloosterman sum K(a). This gives a simple description of zeros of such Kloosterman sums.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Exact Divisibility of Exponential Sums and Some Consequences

In this paper we compute the exact divisibility of some exponential sums over Fp. Our results imply that these families of polynomials are not permutation polynomials of Fp. Also, we apply our results to the Waring problem.

متن کامل

Character Sums with Division Polynomials

We obtain nontrivial estimates of quadratic character sums of division polynomials Ψn(P ), n = 1, 2, . . ., evaluated at a given point P on an elliptic curve over a finite field of q elements. Our bounds are nontrivial if the order of P is at least q for some fixed ε > 0. This work is motivated by an open question about statistical indistinguishability of some cryptographically relevant sequenc...

متن کامل

On Kloosterman sums over finite fields of characteristic 3

We study the divisibility by 3 of Kloosterman sums K(a) over finite fields of characteristic 3. We give a simple recurrent algorithm for finding the largest k, such that 3 divides the Kloosterman sum K(a). This gives a simple description of zeros of such Kloosterman sums.

متن کامل

Divisibility of polynomials over finite fields and combinatorial applications

Consider a maximum-length shift-register sequence generated by a primitive polynomial f over a finite field. The set of its subintervals is a linear code whose dual code is formed by all polynomials divisible by f . Since the minimum weight of dual codes is directly related to the strength of the corresponding orthogonal arrays, we can produce orthogonal arrays by studying divisibility of polyn...

متن کامل

Power sums of polynomials over finite fields and applications: A survey

In this brief expository survey, we explain some results and conjectures on various aspects of the study of the sums of integral powers of monic polynomials of a given degree over a finite field. The aspects include non-vanishing criteria, formulas and bounds for degree and valuation at finite primes, explicit formulas of various kind for the sums themselves, factorizations of such sums, genera...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Des. Codes Cryptography

دوره 66  شماره 

صفحات  -

تاریخ انتشار 2013