Information on Result #1014735

Linear OOA(8161, 5592574, F8, 3, 18) (dual of [(5592574, 3), 16777561, 19]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(823, 172, F8, 3, 9) (dual of [(172, 3), 493, 10]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(823, 516, F8, 9) (dual of [516, 493, 10]-code), using
      • construction X applied to Ce(8) ⊂ Ce(6) [i] based on
        1. linear OA(822, 512, F8, 9) (dual of [512, 490, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
        2. linear OA(819, 512, F8, 7) (dual of [512, 493, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
        3. linear OA(81, 4, F8, 1) (dual of [4, 3, 2]-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(8161, 1864191, F8, 21, 18) (dual of [(1864191, 21), 39147850, 19]-NRT-code) [i]OOA Folding and Stacking with Additional Row