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A new approach on the computation of the nonlinear span of periodic binary sequences, i.e. the length of shortest feedback shift register that generates the given sequence, is presented. The problem of designing binary sequences with the maximum possible span is considered and solved
In this paper, for integers e and n such that e|n and 2e - 1 is a prime, we propose a method of constructing binary low correlation zone (LCZ) sequences of period 2n - 1 by using the extended form sequence with the same period. These new LCZ sequences use Legendre sequences as their column sequences
Binary sequences where successive ones are separated by at most k consecutive zeros, are said to be k-constrained. We introduce a new fixed-rate algorithm for efficiently encoding and decoding k-constrained sequences. Our approach is based on bit stuffing proposed by Bender and Wolf. Bit stuffing is a simple algorithm that can produce near-optimal codes for a wide range of constraints. While bit stuffing...
In this paper, given a composite integer n, we propose a method of constructing quaternary low correlation zone (LCZ) sequences of period 2 n $1 from binary sequences of the same length with ideal autocorrelation. These new sequences are optimal with respect to the bound by Tang, Fan, and Matsufuji. The correlation distributions of these new quaternary LCZ sequences constructed from m-sequences and...
We investigate the optimal Hamming distance that is achievable when mapping binary sequences to permutation sequences. This is used to determine how close to optimum some of the known mappings are. Furthermore, using simulation results we show that mappings found by exhaustive search using optimum distance as criterion perform better than previous known mappings
Linear equations have always been powerful tools in cryptanalysis. In this paper, we present a general linear equation in the binary alphabet of minimum weight 3 that holds for all state lengths and all shifts of sequences generated by the T-function proposed by Klimov and Shamir. It is surprising that these linear properties exist, and they indicate that the T-functions are not as 'wild' and non-algebraic...
The Groebner basis calculation algorithms were successfully applied to construct new sequences analytically. New unimodular perfect sequences with 6 phases were proposed for various sequence lengths. For perfect root-of-unity sequences and for binary sequences with ideal autocorrelation this new approach was used to find sequences analytically. Although this approach was not able to find previously...
Data compression techniques such as Shannon-Fano-Elias coding are often used in conjunction with cryptography. We discuss using Shannon-Fano-Elias codes for encryption. We focus mainly on the problem of deciphering a binary sequence that has been Shannon-Fano-Elias encoded. We show that if a cryptanalyst knows the source symbols and the probability mass function (PMF), then the Shannon-Fano-Elias...
We present bit-stuffing schemes which encode arbitrary data sequences into two-dimensional (2-D) constrained arrays. We consider the class of 2-D runlength-limited (RLL) (d, infin) constraints as well as the 'no isolated bits' (n.i.b.) constraint, both defined on the square lattice. The bit stuffing technique was previously introduced and applied to the class of 2-D (d, infin) constraints. Analytical...
Communications over a binary channel with an additive (modulo 2) individual noise sequence and a full causal feedback link is explored. A randomized sequential transmission scheme that adapts its rate to the individual noise realization is presented. The decoding rate is analyzed for a special case, and shown to asymptotically approach 1 - hb (pemp) with a vanishing probability of error w.r.t. the...
In this paper, we derive the cyclotomic numbers of order 5 over an extension field Fpn using the well-known results of quintic Jacobi sums over Fp (B. C. Berndt, et al., 1998). For p ne 1 mod 5, we have obtained the simple closed-form expression of the cyclotomic numbers of order 5 over Fpn. For p equiv 1 mod 5, we express the cyclotomic number of order 5 over F pn in terms of the solution of the...
We present a simple modification of the Berlekamp-Massey (BM) algorithm by which one can solve the problem solved by the 'multiple-sequence BM algorithm' [Feng and Tzeng, IEEE IT Trans. 1989, 1991]. The original BM algorithm which we call 'single-sequence BM algorithm' finds a simplest linear feedback shift register (LFSR) capable of generating a given (single) sequence while the multiple-sequence...
Recently Xing et al constructed some families of binary sequences with low correlation and large linear complexity by making use of the theory of Artin-Schreier extensions of function fields. In this paper, we present a new construction by using the theory of Kummer extensions of function fields. The analysis shows than they have large periods, large linear complexities, and low correlations. In some...
This paper describes the synthesis of matrices with good correlation, from cyclic shifts of pseudonoise columns. Optimum matrices result whenever the shift sequence satisfies the constant difference property. Known shift sequences with the constant (or almost constant) difference property are: quadratic (polynomial) and reciprocal shift modulo prime, exponential shift, Legendre shift, Zech logarithm...
We obtain bounds on the probability that the n'th variable in a stationary random process differs from all previous ones, and use it to show that the pattern entropy rate of any finite-entropy stationary process equals the process entropy rate. In the particular case of i.i.d. processes we also bound the speed at which the per-symbol pattern entropy converges to the sequence entropy
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