Information on Result #1014304

Linear OOA(876, 5592660, F8, 3, 9) (dual of [(5592660, 3), 16777904, 10]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(810, 258, F8, 3, 4) (dual of [(258, 3), 764, 5]-NRT-code), using
    • OA 2-folding and stacking [i] based on linear OA(810, 516, F8, 4) (dual of [516, 506, 5]-code), using
      • discarding factors / shortening the dual code based on linear OA(810, 517, F8, 4) (dual of [517, 507, 5]-code), using
        • construction XX applied to C1 = C([510,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([510,2]) [i] based on
          1. linear OA(87, 511, F8, 3) (dual of [511, 504, 4]-code or 511-cap in PG(6,8)), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [i]
          2. linear OA(87, 511, F8, 3) (dual of [511, 504, 4]-code or 511-cap in PG(6,8)), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
          3. linear OA(810, 511, F8, 4) (dual of [511, 501, 5]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
          4. linear OA(84, 511, F8, 2) (dual of [511, 507, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
          5. linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code), using
          6. linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code) (see above)
  2. linear OOA(866, 5592402, F8, 3, 9) (dual of [(5592402, 3), 16777140, 10]-NRT-code), using
    • trace code [i] based on linear OOA(6433, 2796201, F64, 3, 9) (dual of [(2796201, 3), 8388570, 10]-NRT-code), using
      • OOA 3-folding [i] based on linear OA(6433, large, F64, 9) (dual of [large, large−33, 10]-code), using
        • the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (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

None.