Information on Result #1014742

Linear OOA(8170, 5593771, F8, 3, 18) (dual of [(5593771, 3), 16781143, 19]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(832, 1369, F8, 3, 9) (dual of [(1369, 3), 4075, 10]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(832, 4107, F8, 9) (dual of [4107, 4075, 10]-code), using
      • construction X applied to Ce(8) ⊂ Ce(5) [i] based on
        1. linear OA(829, 4096, F8, 9) (dual of [4096, 4067, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
        2. linear OA(821, 4096, F8, 6) (dual of [4096, 4075, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
        3. linear OA(83, 11, F8, 2) (dual of [11, 8, 3]-code), using
  2. linear OOA(8138, 5592402, F8, 3, 18) (dual of [(5592402, 3), 16777068, 19]-NRT-code), using
    • trace code [i] based on linear OOA(6469, 2796201, F64, 3, 18) (dual of [(2796201, 3), 8388534, 19]-NRT-code), using
      • OOA 3-folding [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
        • the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [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(8170, 1864590, F8, 21, 18) (dual of [(1864590, 21), 39156220, 19]-NRT-code) [i]OOA Folding and Stacking with Additional Row