On the cross-combined measure of families of binary lattices and sequences

Gyarmati, Katalin (2018) On the cross-combined measure of families of binary lattices and sequences. In: Number-Theoretic Methods in Cryptology. Lecture Notes in Computer Science (10737). Springer, pp. 217-238.


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The cross-combined measure (which is a natural extension of cross-correlation measure) is introduced and important constructions of large families of binary lattices with optimal or nearly optimal cross-combined measures are presented. These results are also strongly related to the one-dimensional case: An easy method is showed obtaining strong constructions of families of binary sequences with nearly optimal cross-correlation measures based on the previous constructions of families of lattices. The important feature of this result is that so far there exists only one type of constructions of very large families of binary sequences with small cross-correlation measure, and this only type of constructions was based on one-variable irreducible polynomials. Since it is very complicated to construct one-variable irreducible polynomials over $\mathbb F_p$, it became necessary to show other types of constructions where the generation of sequences is much faster. Using binary lattices based on two-variable irreducible polynomials this problem can be avoided. (Since, contrary to one-variable polynomials, using Sch\"oneman-Eisenstein criteria it is possible to generate two-variable irreducible polynomials over $\mathbb F_p$ fast.)

Item Type: Book Section
Additional Information: First International Conference, NuTMiC 2017, Warsaw, Poland, September 11-13, 2017
Subjects: Q Science / természettudomány > QA Mathematics / matematika > QA71 Number theory / számelmélet
Depositing User: Katalin Gyarmati
Date Deposited: 28 Jan 2019 11:00
Last Modified: 28 Jan 2019 11:00

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