Information on Result #731890

Linear OA(8144, 2097233, F8, 21) (dual of [2097233, 2097089, 22]-code), using (u, u+v)-construction based on
  1. linear OA(816, 65, F8, 10) (dual of [65, 49, 11]-code), using
    • the BCH-code C(I) with length 65 | 84−1, defining interval I = {1,8,15,…,64}, and designed minimum distance d ≥ |I|+1 = 11 [i]
  2. linear OA(8128, 2097168, F8, 21) (dual of [2097168, 2097040, 22]-code), using
    • construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
      1. linear OA(8127, 2097153, F8, 21) (dual of [2097153, 2097026, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
      2. linear OA(8113, 2097153, F8, 19) (dual of [2097153, 2097040, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
      3. linear OA(81, 15, F8, 1) (dual of [15, 14, 2]-code), using

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(8144, 1048616, F8, 2, 21) (dual of [(1048616, 2), 2097088, 22]-NRT-code) [i]OOA Folding
2Linear OOA(8144, 699077, F8, 3, 21) (dual of [(699077, 3), 2097087, 22]-NRT-code) [i]
3Linear OOA(8144, 209723, F8, 21, 21) (dual of [(209723, 21), 4404039, 22]-NRT-code) [i]OOA Folding and Stacking with Additional Row