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We study a discrete model of repelling particles, and we show using linear programming bounds that many familiar families of error-correcting codes minimize a broad class of potential energies when compared with all other codes of the same size and block length.
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T. Helleseth, T. Kløve, and V. I. Levenshtein, “The simplex codes and other even-weight binary linear codes for error correction,” IEEE Trans. Inf. Theory , vol. 50, no. 11, pp. 2818–2823, Nov. 2004, doi: 10.1109/TIT.2004.836708
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R. J. McEliece, The Theory of Information and Coding , student edition. Cambridge, U.K.: Cambridge University Press, 2004, doi: 10.1017/CBO9780511819896
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A. Schrijver, “New code upper bounds from the Terwilliger algebra and semidefinite programming,” IEEE Trans. Inf. Theory , vol. 51, no. 8, pp. 2859–2866, Aug. 2005, doi: 10.1109/TIT.2005.851748
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H. Cohn and J. Woo, “Three-point bounds for energy minimization,” J. Amer. Math. Soc. , vol. 25, no. 4, pp. 929–958, Oct. 2012, doi: 10.1090/S0894-0347-2012-00737-1
2012
Closest in time.
N. Bouman, J. Draisma, and J. van Leeuwaarden, “Energy minimization of repelling particles on a toric grid,” SIAM J. Discrete Math. , vol. 27, no. 3, pp. 1295–1312, 2013, doi: 10.1137/120869067
2013
Closest in time.