Biprefix codes and semisimple algebras
We show here that there exists a close connection between the languagetheoretic concept of biprefixity and the classical algebraic concept of semisimplicity. More precisely, the main result is that, under suitable hypothesis, a (variablelength) code is biprefix if and only if its syntactic algebra is semisimple.
KeywordsFormal Power Series Nilpotent Ideal Finite Codimension Semisimple Algebra Regular Code
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