A Family of Binary Sequences with Optimal Correlation Property and Large Linear Span

A family of binary sequences is presented and proved to have optimal correlation property and large linear span. It includes the small set of Kasami sequences, No sequence set and TN sequence set as special cases. An explicit lower bound expression on the linear span of sequences in the family is given. With suitable choices of parameters, it is proved that the family has exponentially larger linear spans than both No sequences and TN sequences. A class of ideal autocorrelation sequences is also constructed and proved to have large linear span.Comment: 21 page

TRACE REPRESENTATION OF LEGENDRE SEQUENCES OF MERSENNE PRIME PERIOD

In this correspondence, it is shown that Legendre sequences of period p can be explicitly represented using the trace function defined on the finite field with 2(n) elements, whenever p = 2(n) - 1 is prime for some n greater than or equal to 3.X1148sciescopu

Trace Representation of Legendre Sequences of Mersenne Prime Period

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