Theory and applications of q-ary interleaved sequences

A new class of q-ary sequences, called interleaved sequence, is introduced. Their periods, shift equivalence, linear spans, and autocorrelation functions are derived. The interleaved sequences include a large number of popular sequences, such as multiplexed sequences, clock-controlled sequences, Kasami (1966) sequences, GMW sequences, geometric sequences, and No (1989) sequences. A special class of the interleaved sequences is constructed by mapping GF(q/sup m/) sequences into GF(q) sequences in terms of different bases of GF(q/sup m/) over GF(q). As an application of the theory of interleaved sequences, some new families of binary pseudo-random sequences are constructed, which have large linear spans, optimal periodic cross/autocorrelation functions, balance, and the rapidly "hopped" properties. A complete comparison of the new family of sequences with the Gold sequence family, the Kasami (small and large set) sequence families, the Bent-function sequence family, and the No sequence family is discussed. This shows that the new sequence families have important advantages for use in spread-spectrum multiple-access communication systems. >

[1]  F. MacWilliams,et al.  Pseudo-random sequences and arrays , 1976, Proceedings of the IEEE.

[2]  T. Kasami.  WEIGHT DISTRIBUTION FORMULA FOR SOME CLASS OF CYCLIC CODES , 1966 .

[3]  William J. Park,et al.  Relationships between m -sequences over GF(q) and GF(qm) , 1989, IEEE Trans. Inf. Theory.

[4]  Harvey Cohn,et al.  A second course in number theory , 1962 .

[5]  Mark Goresky,et al.  Cascaded GMW sequences , 1993, IEEE Trans. Inf. Theory.

[6]  Solomon W. Golomb,et al.  Two-dimensional synchronization patterns for minimum ambiguity , 1982, IEEE Trans. Inf. Theory.

[7]  R. A. Games.  An algebraic construction of sonar sequences using M -sequences , 1987 .

[8]  Richard A. Games,et al.  On the linear span of binary sequences obtained from q-ary m-sequences, q odd , 1990, IEEE Trans. Inf. Theory.

[9]  M.B. Pursley,et al.  Crosscorrelation properties of pseudorandom and related sequences , 1980, Proceedings of the IEEE.

[10]  S. M. Jennings,et al.  Multiplexed Sequences: Some Properties of the Minimum Polynomial , 1982, EUROCRYPT.

[11]  P. Vijay Kumar,et al.  A new family of binary pseudorandom sequences having optimal periodic correlation properties and large linear span , 1989, IEEE Trans. Inf. Theory.

[12]  Lloyd R. Welch,et al.  Lower bounds on the maximum cross correlation of signals (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[13]  S. Golomb,et al.  Constructions and properties of Costas arrays , 1984, Proceedings of the IEEE.

[14]  Leopold Bömer,et al.  Complex sequences over GF(pM) with a two-level autocorrelation function and a large linear span , 1992, IEEE Trans. Inf. Theory.

[15]  N. Zierler.  Linear Recurring Sequences , 1959 .

[16]  Richard A. Games,et al.  Crosscorrelation of M-sequences and GMW-sequences with the same primitive polynomial , 1985, Discret. Appl. Math..

[17]  John J. Komo,et al.  Primitive polynomials and M-sequences over GF(qm) , 1993, IEEE Trans. Inf. Theory.

[18]  Steven A. Tretter.  Properties of PN2 sequences (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[19]  Thomas Beth,et al.  The Stop-and-Go Generator , 1985, EUROCRYPT.

[20]  R. Scholtz,et al.  GMW sequences (Corresp.) , 1984 .

[21]  Robert A. Scholtz,et al.  Bent-function sequences , 1982, IEEE Trans. Inf. Theory.

[22]  Rudolf Lide,et al.  Finite fields , 1983 .

[23]  Richard A. Games,et al.  On the Linear Span of binary Sequences Obtained from Finite Geometries , 1986, CRYPTO.

[24]  S. M. Jennings.  Autocorrelation function of the multiplexed sequence , 1984 .

[25]  Dieter Gollmann,et al.  Clock-controlled shift registers: a review , 1989, IEEE J. Sel. Areas Commun..