Information on Result #714911

Linear OA(8147, 578, F8, 46) (dual of [578, 431, 47]-code), using construction X applied to C([0,45]) ⊂ C([0,29]) based on
  1. linear OA(8121, 511, F8, 46) (dual of [511, 390, 47]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,45], and designed minimum distance d ≥ |I|+1 = 47 [i]
  2. linear OA(879, 511, F8, 30) (dual of [511, 432, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
  3. linear OA(826, 67, F8, 15) (dual of [67, 41, 16]-code), using
    • construction XX applied to C1 = C([62,12]), C2 = C([0,13]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([62,13]) [i] based on
      1. linear OA(824, 63, F8, 14) (dual of [63, 39, 15]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−1,0,…,12}, and designed minimum distance d ≥ |I|+1 = 15 [i]
      2. linear OA(824, 63, F8, 14) (dual of [63, 39, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
      3. linear OA(826, 63, F8, 15) (dual of [63, 37, 16]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−1,0,…,13}, and designed minimum distance d ≥ |I|+1 = 16 [i]
      4. linear OA(822, 63, F8, 13) (dual of [63, 41, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
      5. linear OA(80, 2, F8, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(80, 2, F8, 0) (dual of [2, 2, 1]-code) (see above)

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(8147, 289, F8, 2, 46) (dual of [(289, 2), 431, 47]-NRT-code) [i]OOA Folding