Methods for relativizing properties of codes

The usual setting for information transmission systems assumes that all words over the source alphabet need to be encoded. The demands on encodings of messages with respect to decodability, error-detection, etc. are thus relative to the whole set of words. In reality, depending on the information source, far fewer messages are transmitted, all belonging to some specific language. Hence the original demands on encodings can be weakened, if only the words in that language are to be considered. This leads one to relativize the properties of encodings or codes to the language at hand. We analyse methods of relativization in this sense. It seems there are four equally convincing notions of relativization. We compare those. Each of them has their own merits for specific code properties. We clarify the differences between the four approaches. We also consider the decidability of relativized properties. If P is a property defining a class of codes and L is a language, one asks, for a given language C, whether C satisfies P relative to L. We show that in the realm of regular languages this question is mostly decidable

Regular autodense languages

A regular component is either autodense or anti-autodense. Characterizations of a regular component being a pure autodense language and being a pure autodense code are obtained. A relationship between intercodes and anti-autodense languages is that for an intercode L of index m, L n is an anti-autodense language for every n > m

A note on autodense related languages

In this paper, some algebraic properties of autodense languages and pure autodense languages are studied. We also investigate the algebraic properties concerning anti-autodense languages. The family of anti-autodense languages contains infix codes, comma-free codes, and some subfamilies of new codes which are anti-autodense prefix codes, anti-autodense suffix codes and anti-autodense codes. The relationships among these subfamilies of new codes are investigated. The characterization of L (n) , n a parts per thousand yen 2, which are anti-autodense is studied