Information on Result #1303221

Linear OA(973, 13134, F9, 18) (dual of [13134, 13061, 19]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(972, 13132, F9, 18) (dual of [13132, 13060, 19]-code), using
    • trace code [i] based on linear OA(8136, 6566, F81, 18) (dual of [6566, 6530, 19]-code), using
      • construction X applied to Ce(17) ⊂ Ce(15) [i] based on
        1. linear OA(8135, 6561, F81, 18) (dual of [6561, 6526, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
        2. linear OA(8131, 6561, F81, 16) (dual of [6561, 6530, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
        3. linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
  2. linear OA(972, 13133, F9, 17) (dual of [13133, 13061, 18]-code), using Gilbert–VarÅ¡amov bound and bm = 972 > Vbs−1(k−1) = 10 428221 995624 204818 030659 988479 301435 566557 242611 828952 674564 319969 [i]
  3. linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(973, 13134, F9, 2, 18) (dual of [(13134, 2), 26195, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(973, 13134, F9, 3, 18) (dual of [(13134, 3), 39329, 19]-NRT-code) [i]
3Digital (55, 73, 13134)-net over F9 [i]
4Linear OOA(973, 6567, F9, 2, 18) (dual of [(6567, 2), 13061, 19]-NRT-code) [i]OOA Folding