Information on Result #1014481

Linear OOA(8122, 5595136, F8, 3, 13) (dual of [(5595136, 3), 16785286, 14]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(824, 2734, F8, 3, 6) (dual of [(2734, 3), 8178, 7]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(824, 8202, F8, 6) (dual of [8202, 8178, 7]-code), using
      • trace code [i] based on linear OA(6412, 4101, F64, 6) (dual of [4101, 4089, 7]-code), using
        • construction X applied to Ce(5) ⊂ Ce(3) [i] based on
          1. linear OA(6411, 4096, F64, 6) (dual of [4096, 4085, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
          2. linear OA(647, 4096, F64, 4) (dual of [4096, 4089, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
          3. linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
  2. linear OOA(898, 5592402, F8, 3, 13) (dual of [(5592402, 3), 16777108, 14]-NRT-code), using
    • trace code [i] based on linear OOA(6449, 2796201, F64, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
      • OOA 3-folding [i] based on linear OA(6449, large, F64, 13) (dual of [large, large−49, 14]-code), using
        • the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (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

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(8122, 2797567, F8, 15, 13) (dual of [(2797567, 15), 41963383, 14]-NRT-code) [i]OOA Folding and Stacking with Additional Row