Information on Result #731941

Linear OA(923, 816, F9, 7) (dual of [816, 793, 8]-code), using (u, u+v)-construction based on
  1. linear OA(94, 82, F9, 3) (dual of [82, 78, 4]-code or 82-cap in PG(3,9)), using
  2. linear OA(919, 734, F9, 7) (dual of [734, 715, 8]-code), using
    • construction XX applied to C1 = C([727,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([727,5]) [i] based on
      1. linear OA(916, 728, F9, 6) (dual of [728, 712, 7]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
      2. linear OA(916, 728, F9, 6) (dual of [728, 712, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
      3. linear OA(919, 728, F9, 7) (dual of [728, 709, 8]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
      4. linear OA(913, 728, F9, 5) (dual of [728, 715, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [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(923, 408, F9, 2, 7) (dual of [(408, 2), 793, 8]-NRT-code) [i]OOA Folding
2Linear OOA(923, 272, F9, 3, 7) (dual of [(272, 3), 793, 8]-NRT-code) [i]