From a GF(q) sequence {a(i)}(i greater than or equal to 0) with period q(n)-1 we can obtain new periodic sequences {(a) over cap(i)$}(i greater than or equal to 0) with period q(n) by inserting one symbol b is an elem...
详细信息
From a GF(q) sequence {a(i)}(i greater than or equal to 0) with period q(n)-1 we can obtain new periodic sequences {(a) over cap(i)$}(i greater than or equal to 0) with period q(n) by inserting one symbol b is an element of GF(q) al the end of each period. Let b(0) = Sigma(i=0)(qn-2) a(i). It is first shown that the linear complexity of {<(a)over cap(i)>}(i greater than or equal to 0), denoted as LC({(a) over cap(i)$}), satisfies LC({(a) over cap(i)$}) = q(n) if b not equal -b(0) and LC({(a) over cap(i)$}) less than or equal to q(n)-1 if b = -b(0). Most of known sequences are shown to satisfy the zero sum property i.e., b(0) = 0. For such sequences satisfying b(0) = 0 it is shown that q(n)-LC({a(i)}) less than or equal to LC({(a) over cap(i)$}) less than or equal to q(n)-1 if b = 0.
We determine the linear complexity of binary sequences derived from the polynomial quotient modulo p defined by F(u) equivalent to f(u) - f(p)(u)/p (mod p), 0 = 0, where f(p)(u) equivalent to f(u) (mod p), for general...
详细信息
We determine the linear complexity of binary sequences derived from the polynomial quotient modulo p defined by F(u) equivalent to f(u) - f(p)(u)/p (mod p), 0 <= F(u) <= p -1, u >= 0, where f(p)(u) equivalent to f(u) (mod p), for general polynomials f(x) epsilon Z[x}. The linear complexity equals to one of the following values [p(2) - p, p(2) - p + 1, p(2) - 1, p(2) - 1, p(2)} if if 2 is a primitive root modulo p(2), depending on p equivalent to 1 or 3 modulo 4 and the number of solutions of f'(u) equivalent to 0 (mod p), where f'(x) is the derivative of f(x). Furthermore, we extend the constructions to d-ary sequences for prime d vertical bar(p - 1) and d being a primitive root modulo p(2).
In this letter we propose a new Whiteman generalized cyclotomic sequence of order 4. Meanwhile, we determine its linear complexity and minimal polynomial. The results show that this sequence possesses both high linear...
详细信息
In this letter we propose a new Whiteman generalized cyclotomic sequence of order 4. Meanwhile, we determine its linear complexity and minimal polynomial. The results show that this sequence possesses both high linear complexity and optimal balance on 1 s and 0 s, which may be attractive for cryptographic applications.
We use polynomial quotients modulo an odd prime p, which are generalized from the Fermat quotients, to define two families of d(>= 2)-ary sequences of period p(2). If d is a primitive element modulo p(2), we determ...
详细信息
We use polynomial quotients modulo an odd prime p, which are generalized from the Fermat quotients, to define two families of d(>= 2)-ary sequences of period p(2). If d is a primitive element modulo p(2), we determine the minimal characteristic polynomials of the sequences and hence their linear complexities, which depend on whether p equivalent to 1 or 3 (mod 4). Moreover, we generalize the result to the polynomial quotients modulo a power of p. (C) 2011 Elsevier B.V. All rights reserved.
The linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are investigated.A new generalized cyclotomic sequence Sof length 2pqis defined with an imbalance p+*** results show th...
详细信息
The linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are investigated.A new generalized cyclotomic sequence Sof length 2pqis defined with an imbalance p+*** results show that this sequence has high linear complexity.
The linear complexity of a de Bruijn sequence is the degree of the shortest linear recursion which generates the sequence. It is well known that the complexity of a binary de Bruijn sequence of length 2(n) is bounded ...
详细信息
The linear complexity of a de Bruijn sequence is the degree of the shortest linear recursion which generates the sequence. It is well known that the complexity of a binary de Bruijn sequence of length 2(n) is bounded below by 2(n-1) + n and above by 2(n-1) for n greater than or equal to 3. We briefly survey the known knowledge in this area. Same new results are also presented, in particular, it is shown that for each interval of length 2(right perpendicular log n left perpendicular + 1), in the above range, there exist binary de Bruijn sequences of length 2(n) with linear complexity in the interval.
It is demonstrated with the Berlekamp-Massey shift-register synthesis algorithm that the linear complexity value of binary complementary sequences is at least 3/4 of the sequence length. For some sequence pairs the li...
详细信息
It is demonstrated with the Berlekamp-Massey shift-register synthesis algorithm that the linear complexity value of binary complementary sequences is at least 3/4 of the sequence length. For some sequence pairs the linear complexity value can be even 0.98 times the sequence length. In the light of these results strongly non-linear complementary sequences are considered suitable for information security applications employing the spread-spectrum (SS) technique.
作者：
Du, XiaoniChen, ZhixiongPutian Univ
Key Lab Appl Math Putian 351100 Fujian Peoples R China NW Normal Univ
Coll Math & Informat Sci Lanzhou 730070 Gansu Peoples R China Xidian Univ
State Key Lab Integrated Serv Networks Xian 710071 Peoples R China
Let p be an odd prime number. We define a family of quaternary sequences of period 2p using generalized cyclotomic classes over the residue class ring modulo 2p. We compute exact values of the linear complexity, which...
详细信息
Let p be an odd prime number. We define a family of quaternary sequences of period 2p using generalized cyclotomic classes over the residue class ring modulo 2p. We compute exact values of the linear complexity, which are larger than half of the period. Such sequences are 'good' enough from the viewpoint of linear complexity.
Let p be an odd prime and w < p be a positive integer. The authors continue to investigate the binary sequence (f(u)) over {0, 1} defined from polynomial quotients by (uw -uwp)/p modulo p. The (f(u)) is generated i...
详细信息
Let p be an odd prime and w < p be a positive integer. The authors continue to investigate the binary sequence (f(u)) over {0, 1} defined from polynomial quotients by (uw -uwp)/p modulo p. The (f(u)) is generated in terms of (- 1) f(u) which equals to the Legendre symbol of (uw -uwp)/p (mod p) for u = 0. In an earlier work, the linear complexity of (f(u)) was determined for w = p - 1 (i. e. the case of Fermat quotients) under the assumption of 2(p-1) /= 1(mod p2). In this work, they develop a naive trick to calculate all possible values on the linear complexity of (f(u)) for all 1 = w < p - 1 under the same assumption. They also state that the case of larger w(= p) can be reduced to that of 0 <= w <= p - 1. So far, the linear complexity is almost determined for all kinds of Legendre-polynomial quotients.
We obtain a new exponential lower bound on the linear complexity of the new pseudo-random function, introduced recently by M. Naor and O. Reingold. This bound is an improvement of the lower bound on the linear complex...
详细信息
We obtain a new exponential lower bound on the linear complexity of the new pseudo-random function, introduced recently by M. Naor and O. Reingold. This bound is an improvement of the lower bound on the linear complexity of this function that has been obtained by F. Griffin and I.E. Shparlinski. (C) 2000 Elsevier Science B.V. All rights reserved.
暂无评论