The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
A new upper bound on the minimal distance of self-dual codes
Abstract
It is shown that the minimal distance d of a binary self-dual code of length n>or=74 is at most 2((n+6)/10). This bound is a consequence of some new conditions on the weight enumerator of a self-dual code obtained by considering a particular translate of the code, called its shadow. These conditions also enable one to find the highest possible minimal distance of a self-dual code for all n>or=60; to show that self-dual codes with dor=22, with d>or=8 exist precisely for n=24, 32 and n>or=26, and with d>or=10 exist precisely for n>or=46; and to show that there are exactly eight self-dual codes of length 32 with d=8. Several of the self-dual codes of length 34 have trivial group (this appears to be the smallest length where this can happen).>
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Cites
The Theory of Error-Correcting Codes
(1977) · North-Holland Mathematical Library · doi:10.1016/s0924-6509(08)x7030-8 · Cited by 10,760
Whittaker, E. T., & Watson, G. N. (2021) · Cambridge University Press eBooks · doi:10.1017/9781009004091 · Cited by 6,850
(2014) · Developing Nonprofit and Human Service Leaders: Essential Knowledge and Skills · doi:10.4135/9781483388007.n5 · Cited by 3,811
Sphere Packings, Lattices and Groups.
Coxeter, H. S. M., Conway, J. H., & Sloane, N. J. A. (1989) · The American Mathematical Monthly · doi:10.2307/2323992 · Cited by 3,377
Self-citation(1916) · Nature · doi:10.1038/097298a0 · Cited by 2,636
Applied and Computational Complex Analysis
Thacher, H. C., & Henrici, P. (1977) · Mathematics of Computation · doi:10.2307/2005805 · Cited by 2,022
Sphere Packings, Lattices and Groups
Conway, J. H., & Sloane, N. J. A. (1988) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-1-4757-2016-7 · Cited by 1,532
Self-citationAsymptotic methods in analysis
de Bruijn, N. G. (1958) · International Linear Collider · Cited by 1,332
New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities
McEliece, R., Rodemich, E., Rumsey, H., & Welch, L. (1977) · IEEE Transactions on Information Theory · doi:10.1109/tit.1977.1055688 · Cited by 447
A new table of constant weight codes
Brouwer, A. E., Shearer, J. B., Sloane, N. J. A., & Smith, W. D. (1990) · IEEE Transactions on Information Theory · doi:10.1109/18.59932 · Cited by 422
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Quantum error correction via codes over GF(4)
Calderbank, A. R., Rains, E. M., Shor, P. M., & Sloane, N. J. A. (1998) · IEEE Transactions on Information Theory · doi:10.1109/18.681315 · Cited by 1,742
Self-citationMultiqubit monogamy relations beyond shadow inequalities
Serrano-Ensástiga, E., Giraud, O., & Martin, J. (2026) · Physical Review A · doi:10.1103/9fkf-hm8l
Metadata
- Authors
- Conway, J. H., & Sloane, N. J. A.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1990
- Volume
- 36
- Issue
- 6
- Pages
- 1319-1333
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2061721328
- Cited by
- 347
- References
- 13
- FWCI
- 3.96
- Type
- journal article
- Language
- en
- Open access
- closed
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