Gyarmati, Katalin (2018) On the crosscombined measure of families of binary lattices and sequences. In: NumberTheoretic Methods in Cryptology. Lecture Notes in Computer Science (10737). Springer, pp. 217238.

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Abstract
The crosscombined measure (which is a natural extension of crosscorrelation measure) is introduced and important constructions of large families of binary lattices with optimal or nearly optimal crosscombined measures are presented. These results are also strongly related to the onedimensional case: An easy method is showed obtaining strong constructions of families of binary sequences with nearly optimal crosscorrelation 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 crosscorrelation measure, and this only type of constructions was based on onevariable irreducible polynomials. Since it is very complicated to construct onevariable 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 twovariable irreducible polynomials this problem can be avoided. (Since, contrary to onevariable polynomials, using Sch\"onemanEisenstein criteria it is possible to generate twovariable irreducible polynomials over $\mathbb F_p$ fast.)
Item Type:  Book Section 

Additional Information:  First International Conference, NuTMiC 2017, Warsaw, Poland, September 1113, 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 
URI:  http://real.mtak.hu/id/eprint/90574 
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