Information on Result #713295

Linear OA(733, 356, F7, 12) (dual of [356, 323, 13]-code), using construction XX applied to C1 = C([340,7]), C2 = C([0,9]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([340,9]) based on
  1. linear OA(725, 342, F7, 10) (dual of [342, 317, 11]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−2,−1,…,7}, and designed minimum distance d ≥ |I|+1 = 11 [i]
  2. linear OA(725, 342, F7, 10) (dual of [342, 317, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
  3. linear OA(731, 342, F7, 12) (dual of [342, 311, 13]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−2,−1,…,9}, and designed minimum distance d ≥ |I|+1 = 13 [i]
  4. linear OA(719, 342, F7, 8) (dual of [342, 323, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
  5. linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
  6. linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-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(733, 356, F7, 2, 12) (dual of [(356, 2), 679, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(733, 356, F7, 3, 12) (dual of [(356, 3), 1035, 13]-NRT-code) [i]
3Digital (21, 33, 356)-net over F7 [i]
4Linear OA(734, 358, F7, 12) (dual of [358, 324, 13]-code) [i]Construction X with VarÅ¡amov Bound
5Linear OOA(733, 178, F7, 2, 12) (dual of [(178, 2), 323, 13]-NRT-code) [i]OOA Folding
6Linear OOA(733, 118, F7, 3, 12) (dual of [(118, 3), 321, 13]-NRT-code) [i]