Involution Solid and Join Codes

Natasha Jonoska, Lila Kari and Kalpana Mahalingam


Abstract

In this paper we study generalizations of the classical notion of solid codes and comma-free codes suggested by DNA based computing. In particular we extend the study of coding properties of languages that avoid certain undesirable Watson-Crick bonds between the words. For an involution function we consider involution codes: $\theta$-solid codes, $\theta$-overlap free and $\theta$-join codes. $($ An involution function $\theta$ is such that $\theta^2 = I$. An involution code refers to any of the generalization of the classical notion of codes in which the identity function is replaced by an involution function.$)$ We formalize and investigate the properties of these codes and study the closure and non-closure properties. Necessary condition for $\theta$-solid codes to be maximal is also given. We also discuss the properties of codes that are not $\theta$-comma free but can be split into subcodes that are $\theta$-comma free. Note that if $\theta$ is the identity function, the $\theta$-solid codes and $\theta$-join codes respectively become the well known solid and join codes respectively.


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