简介：SupposeQ（ζm）isthem-thcyclotomicnumberfield,whereζmisanm-thprimitiverootofunity,m>1anyinteger.Letam=ζm+ζm2+...+ζm（m-1）/2ifmisoddandletβmbetheproductoftheintegersl-ζm（1

简介：TheexpressionofcyclotomicpolynomialΦ_(pq)(x)isconcernedforalongtime.AsimpleandexplicitexpressionofΦ_(pq)(x)inZ[x]hasbeenshowed.TheformofthefactorsofΦ_(pq)(x)overF_2andtheupper,lowerboundsoftheirHammingweightareprovided.

简介：Klapper(1994)showedthatthereexistsaclassofgeometricsequenceswiththemaximalpossiblelinearcomplexitywhenconsideredassequencesoverGF(2),butthesesequenceshaveverylowlinearcomplexitieswhenconsideredassequencesoverGF(p)(pisanoddprime).ThislinearcomplexityofabinarysequencewhenconsideredasasequenceoverGF(p)iscalledGF(p)complexity.ThisindicatesthatthebinarysequenceswithhighGF(2)linearcomplexitiesareinadequateforsecurityinthepracticalapplication,while,theirGF(p)linearcomplexitiesarealsoequallyimportant,evenwhentheonlyconcerniswithattacksusingtheBerlekamp-Masseyalgorithm[Massey,J.L.,Shift-registersynthesisandbchdecoding,IEEETransactionsonInformationTheory,15(1),1969,122–127].Fromthisperspective,inthispapertheauthorsstudytheGF(p)linearcomplexityofHall’ssexticresiduesequencesandsomeknowncyclotomic-set-basedsequences.