Information on Result #1013753

Linear OOA(782, 5592576, F7, 3, 8) (dual of [(5592576, 3), 16777646, 9]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(710, 174, F7, 3, 4) (dual of [(174, 3), 512, 5]-NRT-code), using
    • OA 2-folding and stacking [i] based on linear OA(710, 348, F7, 4) (dual of [348, 338, 5]-code), using
      • construction XX applied to C1 = C([341,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([341,2]) [i] based on
        1. linear OA(77, 342, F7, 3) (dual of [342, 335, 4]-code or 342-cap in PG(6,7)), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [i]
        2. linear OA(77, 342, F7, 3) (dual of [342, 335, 4]-code or 342-cap in PG(6,7)), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
        3. linear OA(710, 342, F7, 4) (dual of [342, 332, 5]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
        4. linear OA(74, 342, F7, 2) (dual of [342, 338, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
        5. linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code), using
        6. linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code) (see above)
  2. linear OOA(772, 5592402, F7, 3, 8) (dual of [(5592402, 3), 16777134, 9]-NRT-code), using
    • trace code [i] based on linear OOA(4936, 2796201, F49, 3, 8) (dual of [(2796201, 3), 8388567, 9]-NRT-code), using
      • OOA 3-folding [i] based on linear OA(4936, large, F49, 8) (dual of [large, large−36, 9]-code), using
        • the expurgated narrow-sense BCH-code C(I) with length 25679568 | 495−1, 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.