The Experts below are selected from a list of 309 Experts worldwide ranked by ideXlab platform
Hong-yeop Song - One of the best experts on this subject based on the ideXlab platform.
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Frequency hopping sequences with optimal partial autocorrelation property
International Symposium onInformation Theory 2004. ISIT 2004. Proceedings., 2004Co-Authors: Yun-pyo Hong, Hong-yeop SongAbstract:We characterize pk-ary (p prime, k integer) generalized m-sequences and generalized GMW sequences of period p2k-1 over a Residue Class ring R=GF(p)[xi]/(xik) with the "strictly" optimal partial Hamming autocorrelation function (HAF)
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Frequency hopping sequences with optimal partial autocorrelation properties
IEEE Transactions on Information Theory, 2004Co-Authors: Yun-pyo Hong, Hong-yeop SongAbstract:We Classify some p/sup k/-ary (p prime, k integer) generalized m-sequences and generalized Gordon-Mills-Welch (GMW) sequences of period p/sup 2k/-1 over a Residue Class ring R=GF(p)[/spl xi/]/(/spl xi//sup k/) having optimal partial Hamming autocorrelation properties. In frequency hopping (FH) spread-spectrum systems, these sequences are useful for synchronizing process. Suppose, for example, that a transmitting p/sup k/-ary FH patterns of period p/sup 2k/-1 are correlated at a receiver. Usually, the length of a correlation window, denoted by L, is shorter than the pattern's overall period. In that case, the maximum value of the out-of-phase Hamming autocorrelation is lower-bounded by /spl lceil/L/p/sup k/+1/spl rceil/ but the Classified sequences achieve this bound with equality for any positive integer L.
Yun-pyo Hong - One of the best experts on this subject based on the ideXlab platform.
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Frequency hopping sequences with optimal partial autocorrelation property
International Symposium onInformation Theory 2004. ISIT 2004. Proceedings., 2004Co-Authors: Yun-pyo Hong, Hong-yeop SongAbstract:We characterize pk-ary (p prime, k integer) generalized m-sequences and generalized GMW sequences of period p2k-1 over a Residue Class ring R=GF(p)[xi]/(xik) with the "strictly" optimal partial Hamming autocorrelation function (HAF)
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Frequency hopping sequences with optimal partial autocorrelation properties
IEEE Transactions on Information Theory, 2004Co-Authors: Yun-pyo Hong, Hong-yeop SongAbstract:We Classify some p/sup k/-ary (p prime, k integer) generalized m-sequences and generalized Gordon-Mills-Welch (GMW) sequences of period p/sup 2k/-1 over a Residue Class ring R=GF(p)[/spl xi/]/(/spl xi//sup k/) having optimal partial Hamming autocorrelation properties. In frequency hopping (FH) spread-spectrum systems, these sequences are useful for synchronizing process. Suppose, for example, that a transmitting p/sup k/-ary FH patterns of period p/sup 2k/-1 are correlated at a receiver. Usually, the length of a correlation window, denoted by L, is shorter than the pattern's overall period. In that case, the maximum value of the out-of-phase Hamming autocorrelation is lower-bounded by /spl lceil/L/p/sup k/+1/spl rceil/ but the Classified sequences achieve this bound with equality for any positive integer L.
Akira Suzuki - One of the best experts on this subject based on the ideXlab platform.
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computation of inverses in Residue Class rings of parametric polynomial ideals
International Symposium on Symbolic and Algebraic Computation, 2009Co-Authors: Yosuke Sato, Akira SuzukiAbstract:For a given polynomial f and an ideal I of a polynomial ring K[X] over a field K, we give a necessary and sufficient condition for I to have a smallest ideal extension J such that f is invertible in the Residue Class ring K[X]/J. If the condition holds, J is shown to be the saturation ideal I:∞. We also show primary decompositions of the ideals I:∞ and I+9fm;:, where m is a natural number such that I:∞ = I:fm, all together forms a primary decomposition of I with no modification. These observations are especially useful for polynomial rings with parameters.
Xiumei Li - One of the best experts on this subject based on the ideXlab platform.
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congruence preserving functions in the Residue Class rings of polynomials over finite fields
Finite Fields and Their Applications, 2020Co-Authors: Xiumei LiAbstract:Abstract In this paper, as an analogue of the integer case, we define congruence preserving functions over the Residue Class rings of polynomials over finite fields. We establish a counting formula for such congruence preserving functions, determine a necessary and sufficient condition under which all congruence preserving functions are also polynomial functions, and characterize such functions.
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polynomial functions in the Residue Class rings of dedekind domains
International Journal of Number Theory, 2019Co-Authors: Xiumei LiAbstract:In this paper, as an extension of the integer case, we define polynomial functions over the Residue Class rings of Dedekind domains, and then we give canonical representations and counting formulas...
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polynomial functions in the Residue Class rings of dedekind domains
arXiv: Number Theory, 2019Co-Authors: Xiumei LiAbstract:In this paper, as an extension of the integer case, we define polynomial functions over the Residue Class rings of Dedekind domains, and then we give canonical representations and counting formulas for such polynomial functions. In particular, we give an explicit formula for the number of polynomial functions over the Residue Class rings of polynomials over finite fields.
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Polynomial functions in the Residue Class rings of polynomials over finite fields
arXiv: Number Theory, 2017Co-Authors: Xiumei LiAbstract:In this paper, as an analogue of the integer case, we define polynomial functions over the Residue Class rings of polynomials over a finite field, and then we give canonical representations and the counting formula for such polynomial functions.
Paul Pollack - One of the best experts on this subject based on the ideXlab platform.
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the least prime quadratic nonResidue in a prescribed Residue Class mod 4
Journal of Number Theory, 2017Co-Authors: Paul PollackAbstract:Abstract For all primes p ≥ 5 , there is a prime quadratic nonResidue q p with q ≡ 3 ( mod 4 ) . For all primes p ≥ 13 , there is a prime quadratic nonResidue q p with q ≡ 1 ( mod 4 ) .