Information on Result #1012041

Linear OOA(4202, 2796546, F4, 3, 19) (dual of [(2796546, 3), 8389436, 20]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(433, 345, F4, 3, 9) (dual of [(345, 3), 1002, 10]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(433, 1035, F4, 9) (dual of [1035, 1002, 10]-code), using
      • construction XX applied to C1 = C([339,345]), C2 = C([337,343]), C3 = C1 + C2 = C([339,343]), and C∩ = C1 ∩ C2 = C([337,345]) [i] based on
        1. linear OA(426, 1023, F4, 7) (dual of [1023, 997, 8]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {339,340,…,345}, and designed minimum distance d ≥ |I|+1 = 8 [i]
        2. linear OA(426, 1023, F4, 7) (dual of [1023, 997, 8]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {337,338,…,343}, and designed minimum distance d ≥ |I|+1 = 8 [i]
        3. linear OA(431, 1023, F4, 9) (dual of [1023, 992, 10]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {337,338,…,345}, and designed minimum distance d ≥ |I|+1 = 10 [i]
        4. linear OA(421, 1023, F4, 5) (dual of [1023, 1002, 6]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {339,340,341,342,343}, and designed minimum distance d ≥ |I|+1 = 6 [i]
        5. linear OA(41, 6, F4, 1) (dual of [6, 5, 2]-code), using
        6. linear OA(41, 6, F4, 1) (dual of [6, 5, 2]-code) (see above)
  2. linear OOA(4169, 2796201, F4, 3, 19) (dual of [(2796201, 3), 8388434, 20]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(4169, large, F4, 19) (dual of [large, large−169, 20]-code), using
      • the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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.