Information on Result #720335

Linear OA(991, 734, F9, 34) (dual of [734, 643, 35]-code), using construction XX applied to C1 = C([727,31]), C2 = C([0,32]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C([727,32]) based on
  1. linear OA(988, 728, F9, 33) (dual of [728, 640, 34]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,31}, and designed minimum distance d ≥ |I|+1 = 34 [i]
  2. linear OA(988, 728, F9, 33) (dual of [728, 640, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
  3. linear OA(991, 728, F9, 34) (dual of [728, 637, 35]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,32}, and designed minimum distance d ≥ |I|+1 = 35 [i]
  4. linear OA(985, 728, F9, 32) (dual of [728, 643, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [i]
  5. linear OA(90, 3, F9, 0) (dual of [3, 3, 1]-code), using
  6. linear OA(90, 3, F9, 0) (dual of [3, 3, 1]-code) (see above)

Mode: Constructive and 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(991, 734, F9, 2, 34) (dual of [(734, 2), 1377, 35]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(991, 734, F9, 3, 34) (dual of [(734, 3), 2111, 35]-NRT-code) [i]
3Digital (57, 91, 734)-net over F9 [i]
4Linear OA(992, 771, F9, 34) (dual of [771, 679, 35]-code) [i]VarÅ¡amov–Edel Lengthening
5Linear OOA(991, 367, F9, 2, 34) (dual of [(367, 2), 643, 35]-NRT-code) [i]OOA Folding