Volume 18, issue 5 (2018)

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Self-dual binary codes from small covers and simple polytopes

Bo Chen, Zhi Lü and Li Yu

Algebraic & Geometric Topology 18 (2018) 2729–2767
Bibliography
1 C Allday, M Franz, V Puppe, Equivariant cohomology, syzygies and orbit structure, Trans. Amer. Math. Soc. 366 (2014) 6567 MR3267019
2 C Allday, V Puppe, Cohomological methods in transformation groups, 32, Cambridge Univ. Press (1993) MR1236839
3 M L Balinski, On the graph structure of convex polyhedra in n–space, Pacific J. Math. 11 (1961) 431 MR0126765
4 A Brøndsted, An introduction to convex polytopes, 90, Springer (1983) MR683612
5 V M Buchstaber, T E Panov, Torus actions and their applications in topology and combinatorics, 24, Amer. Math. Soc. (2002) MR1897064
6 B Chen, Z Lü, Equivariant cohomology and analytic descriptions of ring isomorphisms, Math. Z. 261 (2009) 891 MR2480763
7 P E Conner, Differentiable periodic maps, 738, Springer (1979) MR548463
8 M W Davis, T Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991) 417 MR1104531
9 A M Gleason, Weight polynomials of self-dual codes and the MacWilliams identities, from: "Actes du Congrès International des Mathématiciens, 3", Gauthier-Villars, Paris (1971) 211 MR0424391
10 M Goresky, R Kottwitz, R MacPherson, Equivariant cohomology, Koszul duality, and the localization theorem, Invent. Math. 131 (1998) 25 MR1489894
11 B Grünbaum, Convex polytopes, 221, Springer (2003) MR1976856
12 M Harada, An extremal doubly even self-dual code of length 112, Electron. J. Combin. 15 (2008) MR2438589
13 S K Houghten, C W H Lam, L H Thiel, J A Parker, The extended quadratic residue code is the only (48,24,12) self-dual doubly-even code, IEEE Trans. Inform. Theory 49 (2003) 53 MR1965886
14 I V Izmest’ev, Three-dimensional manifolds defined by a coloring of the faces of a simple polytope, Mat. Zametki 69 (2001) 375 MR1846836
15 M Joswig, Projectivities in simplicial complexes and colorings of simple polytopes, Math. Z. 240 (2002) 243 MR1900311
16 G Kalai, A simple way to tell a simple polytope from its graph, J. Combin. Theory Ser. A 49 (1988) 381 MR964396
17 M Kreck, V Puppe, Involutions on 3–manifolds and self-dual, binary codes, Homology Homotopy Appl. 10 (2008) 139 MR2434933
18 J H van Lint, Introduction to coding theory, 86, Springer (1992) MR1217490
19 C L Mallows, N J A Sloane, An upper bound for self-dual codes, Information and Control 22 (1973) 188 MR0414223
20 J Milnor, Construction of universal bundles, II, Ann. of Math. 63 (1956) 430 MR0077932
21 M A Perles, Results and problems on reconstruction of polytopes, unpublished manuscript (1970)
22 V Puppe, Group actions and codes, Canad. J. Math. 53 (2001) 212 MR1814971
23 E M Rains, N J A Sloane, Self-dual codes, from: "Handbook of coding theory, I" (editors V S Pless, W C Huffman, R A Brualdi), North-Holland (1998) 177 MR1667939
24 G C Shephard, A theorem on cyclic polytopes, Israel J. Math. 6 (1968) 368 MR0244856
25 N J A Sloane, Is there a (72,36) d = 16 self-dual code ?, IEEE Trans. Information Theory 19 (1973) 251 MR0421849
26 S Zhang, On the nonexistence of extremal self-dual codes, Discrete Appl. Math. 91 (1999) 277 MR1670195