Spread spectrum communications; vols. 1-3
Spread spectrum communications; vols. 1-3
Finite field for scientists and engineers
Finite field for scientists and engineers
Almost perfect nonlinear power functions on GF (2n): the Niho case
Information and Computation
A New Family of Ternary Sequences with IdealTwo-level Autocorrelation Function
Designs, Codes and Cryptography
Handbook of Coding Theory
A Generalization of Niho's Theorem
Designs, Codes and Cryptography
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Large families of quaternary sequences with low correlation
IEEE Transactions on Information Theory
Some new three-valued crosscorrelation functions for binary m-sequences
IEEE Transactions on Information Theory
Improved binary codes and sequence families from Z4-linear codes
IEEE Transactions on Information Theory
Almost perfect nonlinear power functions on GF(2n): the Welch case
IEEE Transactions on Information Theory
Binary m-sequences with three-valued crosscorrelation: a proof of Welch's conjecture
IEEE Transactions on Information Theory
On a conjectured ideal autocorrelation sequence and a related triple-error correcting cyclic code
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
New families of binary sequences with low correlation
IEEE Transactions on Information Theory
A new family of nonbinary sequences with three-level correlation property and large linear span
IEEE Transactions on Information Theory
Niho type cross-correlation functions via dickson polynomials and Kloosterman sums
IEEE Transactions on Information Theory
A new binary sequence family with low correlation and large size
IEEE Transactions on Information Theory
Cross correlation of m-sequences of different lengths
IEEE Transactions on Information Theory
d-form sequences: families of sequences with low correlation values and large linear spans
IEEE Transactions on Information Theory
New pairs of m-sequences with 4-level cross-correlation
Finite Fields and Their Applications
A Proof of the Welch and Niho Conjectures on Cross-Correlations of Binary m-Sequences
Finite Fields and Their Applications
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In direct-sequence code-division multiple-access (DS-CDMA) communication systems and direct-sequence ultra wideband (DS-UWB) radios, sequences with low correlation and large family size are important for reducing multiple access interference (MAI) and accepting more active users, respectively. In this paper, a new collection of families of sequences of length pn-1, which includes three constructions, is proposed. The maximum number of cyclically distinct families without GMW sequences in each construction is π(pn-1)/n · π(pm-1)/ m, where p is a prime number, n is an even number, and n = 2m, and these sequences can be binary or polyphase depending upon choice of the parameter p. In Construction I, there are pn distinct sequences within each family and the new sequences have at most d + 2 nontrivial periodic correlation {-pm-1, -1, pm-1,2pm-1,···,dpm-1}. In Construction II, the new sequences have large family size p2n and possibly take the nontrivial correlation values in {-pm-1, -1, pm-1, 2pm-1,···,(3d-4)pm-1}. In Construction III, the new sequences possess the largest family size p(d-1)n and have at most 2d correlation levels {-pm-1, -1, pm-1,2pm-1, ···,(2d-2)pm-1}. Three constructions are near-optimal with respect to the Welch bound because the values of their Welch-Ratios are moderate, WR ≐ d, WR ≐ 3d-4 and WR ≐ 2d-2, respectively. Each family in Constructions I, II and III contains a GMW sequence. In addition, Helleseth sequences and Niho sequences are special cases in Constructions I and III, and their restriction conditions to the integers m and n, pm ≠ 2 (mod 3) and n ≡ 0 (mod 4), respectively, are removed in our sequences. Our sequences in Construction III include the sequences with Niho type decimation 3 · 2m-2, too. Finally, some open questions are pointed out and an example that illustrates the performance of these sequences is given.