Information on Result #1014691

Linear OOA(8162, 5595136, F8, 3, 17) (dual of [(5595136, 3), 16785246, 18]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(832, 2734, F8, 3, 8) (dual of [(2734, 3), 8170, 9]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(832, 8202, F8, 8) (dual of [8202, 8170, 9]-code), using
      • trace code [i] based on linear OA(6416, 4101, F64, 8) (dual of [4101, 4085, 9]-code), using
        • construction X applied to Ce(7) ⊂ Ce(5) [i] based on
          1. linear OA(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
          2. linear OA(6411, 4096, F64, 6) (dual of [4096, 4085, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
          3. linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
  2. linear OOA(8130, 5592402, F8, 3, 17) (dual of [(5592402, 3), 16777076, 18]-NRT-code), using
    • trace code [i] based on linear OOA(6465, 2796201, F64, 3, 17) (dual of [(2796201, 3), 8388538, 18]-NRT-code), using
      • OOA 3-folding [i] based on linear OA(6465, large, F64, 17) (dual of [large, large−65, 18]-code), using
        • the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [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(8163, 5595136, F8, 3, 17) (dual of [(5595136, 3), 16785245, 18]-NRT-code) [i]OOA Duplication