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DEMONSTRATIO MATHEMATICAVol. XXXIINo 31999Jerzy ZurawieckiT H E U P P E R B O U N D S OF A F E E D B A C K F U N C T I O N1. IntroductionThe feedback functions and the corresponding recurring sequences —having numerous applications, for instance in coding theory, in cryptography or in several branches of electrical engineering — have been studiedwith methods of linear algebra, ideal theory or formal power series [3], [5].In 1963 Yoeli [10] published two theorems dealing with sequences joiningand a sequence splitting. This has led to a design of algorithms for findingthe Hamiltonian circuits in a de Bruijn graph (cf. [2], [9], [11]). In moregeneral case, the paper [10] yields a tool for studying connections betweenthe feedback functions and allows us to describe them as the elements of apartially ordered set. For a study of this order it is convenient to investigatethe families of upper bounds and lower bounds of a feedback function.As it has been stated in [8], the family of lower bounds of a feedbackfunction — which forms an upper semilattice — is described by a binaryrelation, called the independent splits relation, closely related to the interlacing relation defined
Demonstratio Mathematica – de Gruyter
Published: Jul 1, 1999
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