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Weight distribution of [72,36,12] doubly-even binary self-dual extended quadratic-residue (or QR) code.
5

%I #10 Aug 21 2024 16:37:52

%S 1,0,0,2982,214065,18303516,462306915,4398818490,16600354155,

%T 25759476488,16600354155,4398818490,462306915,18303516,214065,2982,0,

%U 0,1

%N Weight distribution of [72,36,12] doubly-even binary self-dual extended quadratic-residue (or QR) code.

%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1977, Chap. 16.

%H C. J. Tjhai and Martin Tomlinson, <a href="https://web.archive.org/web/20170312040938/http://www.tech.plym.ac.uk/Research/fixed_and_mobile_communications/links/weightdistributions.htm">Weight Distributions of Quadratic Residue and Quadratic Double Circulant Codes over GF(2)</a>.

%e The actual weight enumerator is x^72 + 2982*x^60*y^12 + 214065*x^56*y^16 + 18303516*x^52*y^20 + 462306915*x^48*y^24 + y^72 + 4398818490*x^44*y^28 + 16600354155*x^40*y^32 + 25759476488*x^36*y^36 + 16600354155*x^32*y^40 + 4398818490*x^28*y^44 + 462306915*x^24*y^48 + 18303516*x^20*y^52 + 214065*x^16*y^56 + 2982*x^12*y^60.

%Y Cf. A018236.

%K nonn,fini,full

%O 0,4

%A _N. J. A. Sloane_, Mar 19 2009

%E Name corrected by _Jon-Lark Kim_, Aug 16 2024