Information on Result #713220

Linear OA(719, 348, F7, 7) (dual of [348, 329, 8]-code), using construction XX applied to C1 = C([341,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([341,5]) based on
  1. linear OA(716, 342, F7, 6) (dual of [342, 326, 7]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
  2. linear OA(716, 342, F7, 6) (dual of [342, 326, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
  3. linear OA(719, 342, F7, 7) (dual of [342, 323, 8]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
  4. linear OA(713, 342, F7, 5) (dual of [342, 329, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [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)

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(719, 348, F7, 2, 7) (dual of [(348, 2), 677, 8]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(719, 348, F7, 3, 7) (dual of [(348, 3), 1025, 8]-NRT-code) [i]
3Digital (12, 19, 348)-net over F7 [i]
4Linear OOA(719, 174, F7, 2, 7) (dual of [(174, 2), 329, 8]-NRT-code) [i]OOA Folding
5Linear OOA(719, 116, F7, 3, 7) (dual of [(116, 3), 329, 8]-NRT-code) [i]