Information on Result #1018708

Linear OOA(8167, 2798390, F81, 3, 14) (dual of [(2798390, 3), 8395103, 15]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(8114, 2189, F81, 3, 7) (dual of [(2189, 3), 6553, 8]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(8114, 6567, F81, 7) (dual of [6567, 6553, 8]-code), using
      • construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
        1. linear OA(8113, 6562, F81, 7) (dual of [6562, 6549, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
        2. linear OA(819, 6562, F81, 5) (dual of [6562, 6553, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
        3. linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
  2. linear OOA(8153, 2796201, F81, 3, 14) (dual of [(2796201, 3), 8388550, 15]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(8153, large, F81, 14) (dual of [large, large−53, 15]-code), using
      • the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(8168, 2798390, F81, 3, 14) (dual of [(2798390, 3), 8395102, 15]-NRT-code) [i]OOA Duplication