Abstract
Free semigroups are of importance in Coding Theory and Chapter 3 opens with a characterization theorem for free semigroups (Theorem 2.3). Next, certain mappings associated with codes are introduced and studied; all of them occur later in characterization theorems. The two code properties of irredundance and precorrecting are defined and characterized; irredundance in Theorem 4.1 and precorrecting in Theorem 4.2. Another characterization of free semigroups is presented in Theorem 4.3. The code property of correcting is defined and characterized in Theorem 5.1 which gives nine statements equivalent to correcting Finally, Theorem 5.4 characterizes correcting in terms of correcting for ‘short’ sentences, a theorem important for algorithms.
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© 1974 D. Reidel Publishing Company, Dordrecht, Holland
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Hartnett, W.E. (1974). Overview. In: Hartnett, W.E. (eds) Foundations of Coding Theory. Episteme, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2298-9_3
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DOI: https://doi.org/10.1007/978-94-010-2298-9_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-2300-9
Online ISBN: 978-94-010-2298-9
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