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An Infinite Class of Balanced Functions with Optimal Algebraic Immunity, Good Immunity to Fast Algebraic Attacks and Good Nonlinearity
TLDR
In this paper, we study an infinite class of functions which achieve an optimum algebraic immunity and a much better nonlinearity. Expand
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Weight distribution of some reducible cyclic codes
TLDR
We determine the weight distribution of the cyclic codes C"1 and C"2 over F"p with parity-check polynomial h"1(x), h"2(x) and h"3(x). Expand
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A finite Gilbert-Varshamov bound for pure stabilizer quantum codes
  • K. Feng, Z. Ma
  • Mathematics, Computer Science
  • IEEE Transactions on Information Theory
  • 1 December 2004
TLDR
A finite Gilbert-Varshamov bound for pure stabilizer (binary and nonbinary) quantum error correcting codes is presented in analogy to the GV bound for classical codes. Expand
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Spectra of Hypergraphs and Applications
Abstract To a regular hypergraph we attach an operator, called its adjacency matrix, and study the second largest eigenvalue as well as the overall distribution of the spectrum of this operator. OurExpand
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Linear error-block codes
TLDR
A linear error-block code is a natural generalization of the classical error-correcting code and has applications in experimental design, high-dimensional numerical integration and cryptography. Expand
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Cyclic Codes and Sequences From Generalized Coulter–Matthews Function
  • Jinquan Luo, K. Feng
  • Mathematics, Computer Science
  • IEEE Transactions on Information Theory
  • 1 December 2008
TLDR
In this paper, we will study the exponential sum SigmaxisinF<sub>q</sub> x(alphax(p<sup>k</sup>+1)/2+betax) that is related to the generalized Coulter-Matthews function x(pk+ 1)/2 with k/gcd. Expand
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On elliptic curves y2=x3−n2x with rank zero
Abstract In this paper we determine all elliptic curves E n : y 2 = x 3 − n 2 x with the smallest 2-Selmer groups S n = Sel 2 ( E n ( Q ))={1} and S n ′= Sel 2 ( E n ′( Q ))={±1,± n }( E n ′: y 2 = xExpand
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Value Distributions of Exponential Sums From Perfect Nonlinear Functions and Their Applications
  • K. Feng, Jinquan Luo
  • Mathematics, Computer Science
  • IEEE Transactions on Information Theory
  • 1 September 2007
TLDR
In this paper we present a unified way to determine the values and their multiplicities of the exponential sums Sigma<sub>xisinF(q)</sub>zeta <sup>Tr(af(x)+bx)</sup>(a,bisinF< sub>q</sub>,q=p<sup>m</sup>,pges3) for all perfect nonlinear functions f which is a Dembowski-Ostrom polynomial. Expand
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Quantum codes [[6, 2, 3]]p and [[7, 3, 3]]p (p >= 3) exist
  • K. Feng
  • Mathematics, Computer Science
  • IEEE Trans. Inf. Theory
  • 1 August 2002
TLDR
We prove that nonbinary quantum stabilizer codes with parameters [[n, k, d]]/sub p/ exist for all odd primes p by using graph machinery, given by Schlingemann and Werner. Expand
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On the Weight Distributions of Two Classes of Cyclic Codes
  • Jinquan Luo, K. Feng
  • Mathematics, Computer Science
  • IEEE Transactions on Information Theory
  • 1 December 2008
TLDR
Let q=p<sup>m</sup> where p is an odd prime, mges2, and 1lesklesm-1. Expand
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