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Completing codes. (English) Zbl 0669.94012
Summary: The problem to characterize those finite codes that can be embedded in a finite maximal code is investigated. The main results, which give some necessary conditions for the embedding, are obtained by using factorizations of cyclic groups.

94B05 Linear codes (general theory)
94B15 Cyclic codes
20K01 Finite abelian groups
Full Text: DOI EuDML
[1] 1. J. BERSTEL and D. PERRIN, The Theory of Codes, Academic Press, 1985. Zbl0587.68066 MR797069 · Zbl 0587.68066
[2] 2. C. DE FELICE, Construction of a Family of Finite Maximal Codes, Report of L.I.T.P., 1987. · Zbl 0664.94022
[3] 3. C. DE FELICE and A. RESTIVO, Some Results on Finite Maximal Codes, R.A.I.R.O. Informatique Théorique, Vol. 19, No. 4, 1985. Zbl0578.68062 MR827484 · Zbl 0578.68062
[4] 4. A. EHRENFEUCHT and G. ROZEMBERG, Each Regular Code is Included in a Maximal Regular Code, R.A.I.R.O. Informat. Theor. Application, Vol. 20, 1986, pp. 89-96. Zbl0609.68053 MR849968 · Zbl 0609.68053
[5] 5. FUCHS, Abelian Group, Pergamon Press, 1960.
[6] 6. Al. A. MARKOV, An Example of an Indipendent System of Words which Cannot be Included in a Finite Complete System (Russian), Mat. Zametki, Vol. 1 1967, pp. 87-90. Zbl0154.00703 MR210594 · Zbl 0154.00703
[7] 7. M. KRASNER and B. RANULAC, Sur une propriété des polynomes de la division du cercle, C.R. Acad. Sci. Paris, T. 204, 1937, pp. 397-399. JFM63.0044.03 · Zbl 0015.38601
[8] 8. D. PERRIN and M. P. SCHUTZENBERGER, Un problème élémentaire de la théorie de l’information, Coll. Internat, du C.N.R.S., n^\circ 276, Théorie de l’Information, 1977. Zbl0483.94028 · Zbl 0483.94028
[9] 9. A. RESTIVO, On Codes Having no Finite Completion, Discrete Math., Vol. 17, 1977, pp. 309-316. Zbl0357.94011 MR498922 · Zbl 0357.94011
[10] 10. P. SHORA Counterexample to the Triangle Conjecture, J. Comb. Theory A, Vol. 38, 1985, pp. 110-112. Zbl0558.20032 MR773566 · Zbl 0558.20032
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