Information on Result #1019349

Linear OOA(12872, 2801665, F128, 3, 15) (dual of [(2801665, 3), 8404923, 16]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(12815, 5464, F128, 3, 7) (dual of [(5464, 3), 16377, 8]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(12815, 16392, F128, 7) (dual of [16392, 16377, 8]-code), using
      • construction X applied to Ce(6) ⊂ Ce(3) [i] based on
        1. linear OA(12813, 16384, F128, 7) (dual of [16384, 16371, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
        2. linear OA(1287, 16384, F128, 4) (dual of [16384, 16377, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
        3. linear OA(1282, 8, F128, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,128)), using
  2. linear OOA(12857, 2796201, F128, 3, 15) (dual of [(2796201, 3), 8388546, 16]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(12857, large, F128, 15) (dual of [large, large−57, 16]-code), using
      • the expurgated narrow-sense BCH-code C(I) with length 15790321 | 1288−1, 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

None.