Information on Result #1014696

Linear OOA(8168, 5603329, F8, 3, 17) (dual of [(5603329, 3), 16809819, 18]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(838, 10927, F8, 3, 8) (dual of [(10927, 3), 32743, 9]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(838, 32781, F8, 8) (dual of [32781, 32743, 9]-code), using
      • 1 times code embedding in larger space [i] based on linear OA(837, 32780, F8, 8) (dual of [32780, 32743, 9]-code), using
        • construction X4 applied to Ce(8) ⊂ Ce(5) [i] based on
          1. linear OA(836, 32768, F8, 9) (dual of [32768, 32732, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
          2. linear OA(826, 32768, F8, 6) (dual of [32768, 32742, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
          3. linear OA(811, 12, F8, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,8)), using
          4. linear OA(81, 12, F8, 1) (dual of [12, 11, 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

None.