Mass formulas for self-dual codes over ℤ4 and Fq + uFq rings

IEEE Transactions on Information Theory

Volumn 42, Issue 4, 1996, Pages 1222-1228

  Gaborit, Philippe ^a  

^a UNIVERSITÉ DE BORDEAUX   (France)

Author keywords

Automorphisms group; Codes over rings; Mass formula; Self dual codes; Type II codes

Indexed keywords

ALGEBRA; BINARY CODES; CLASSIFICATION (OF INFORMATION); COMPUTATION THEORY; EQUIVALENCE CLASSES; INFORMATION THEORY; THEOREM PROVING;

AUTOMORPHISMS GROUP; CODES OVER RINGS; MASS FORMULAS; SELF DUAL CODES;

CODES (SYMBOLS);

EID: 0030192130     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.508845     Document Type: Article

References (12)

1. C. Bachoc, "Voisinage au sens de Kneser pour les Réseaux Quaternioniens," Comm. Math. Helv., vol. 70, pp. 350-374, 1995.
2. _, "Applications of coding theory to the construction of modular lattices," in preparation.
3. A. Bonnecaze and P. Solé, Quaternary Type II Codes, to appear.
4. A. R. Caldebank, A. R. Hammons Jr., P. V. Kumar, N. J. A. Sloane, and P. Solé, "Quaternary construction of formally linear construction for certain Kerdock arid Preparata codes," Bull. Amer. Math. Soc. (new series), vol. 29, no. 2, pp. 218-222, 1993.
5. A. R. Calderbank, "A Gilbert-Varshamov bound for even unimodular lattices," to appear.
6. J. H. Conway and N. J. A. Sloane, "Self-dual codes over the integers modulo 4," J. Comb. Theory, vol. A, no. 62, pp. 31-45, 1993.
7. M. Klemm, "Selbstduale Codes uber dem Ring der ganzen Zahlen modulo 4," Arch. Math., vol. 53, pp. 201-207, 1989.
8. F. J. MacWilliams, A. M. Odlyzko, N. J. A. Sloane, and H. N. Ward, "Self-duals codes over GF(4)," J. Comb. Theory, vol. A, no. 25 pp. 288-318, 1978.
9. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North-Holland, 1977.
10. F. J. MacWilliams, N. J. A. Sloane, and J. G. Thompson, "Good self-dual codes exist," Discr. Math., vol. 3, pp. 153-162, 1972.
11. V. Pless, 'The number of isotropic subspaces in a finite geometry." Atti. Accad. Naz. Lincei Rendic., vol. 39, pp. 418-421, 1965.
12. D. A. Taylor, "The geometry of classical groups," Sigma Series in Pure Math., vol. 9. Berlin, Germany: Heldermann-Verlag, 1992.