Information on Result #1014264

Linear OOA(868, 5592660, F8, 3, 8) (dual of [(5592660, 3), 16777912, 9]-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(858, 5592402, F8, 3, 8) (dual of [(5592402, 3), 16777148, 9]-NRT-code), using
    • trace code [i] based on linear OOA(6429, 2796201, F64, 3, 8) (dual of [(2796201, 3), 8388574, 9]-NRT-code), using
      • OOA 3-folding [i] based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
        • the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [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.