Information on Result #1014586

Linear OOA(8146, 5603329, F8, 3, 15) (dual of [(5603329, 3), 16809841, 16]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(832, 10927, F8, 3, 7) (dual of [(10927, 3), 32749, 8]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(832, 32781, F8, 7) (dual of [32781, 32749, 8]-code), using
      • construction X4 applied to C([0,3]) ⊂ C([0,2]) [i] based on
        1. linear OA(831, 32769, F8, 7) (dual of [32769, 32738, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
        2. linear OA(821, 32769, F8, 5) (dual of [32769, 32748, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [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(8114, 5592402, F8, 3, 15) (dual of [(5592402, 3), 16777092, 16]-NRT-code), using
    • trace code [i] based on linear OOA(6457, 2796201, F64, 3, 15) (dual of [(2796201, 3), 8388546, 16]-NRT-code), using
      • OOA 3-folding [i] based on linear OA(6457, large, F64, 15) (dual of [large, large−57, 16]-code), using
        • the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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(8147, 5603329, F8, 3, 15) (dual of [(5603329, 3), 16809840, 16]-NRT-code) [i]OOA Duplication