Ex­ten­ded Af­fi­ne and CCZ Equi­va­lence up to Di­men­si­on 4

Mar­cus Brink­mann

A com­ple­te clas­si­fi­ca­ti­on of all vec­to­ri­al boo­le­an func­tions in up to di­men­si­on 4, up to ex­ten­ded af­fi­ne and CCZ equi­va­lence. Work done as part of my di­plo­ma the­sis in 2008, and since then cited as per­so­nal com­mu­ni­ca­ti­on.

Ab­stract

For all vec­to­ri­al boo­le­an func­tions up to di­men­si­on 4, we pre­sent ca­no­ni­cal re­pre­sen­ta­ti­ves for all ex­ten­ded af­fi­ne (EA) and CCZ equi­va­lence clas­ses. We in­clu­de the size of each class, as well as its al­ge­braic de­gree and ex­ten­ded Walsh spec­trum. We also an­s­wer the fol­lowing ques­ti­ons: How large are these clas­ses? Which of these clas­ses con­tain bi­jec­tive func­tions? And how are these clas­ses grou­ped into CCZ equi­va­lence clas­ses?

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Tags: ccz equi­va­lence, ex­ten­ded af­fi­ne equi­va­lence, vec­to­ri­al boo­le­an func­tions