Information on Result #713495

Linear OA(751, 356, F7, 19) (dual of [356, 305, 20]-code), using construction XX applied to C1 = C([340,14]), C2 = C([0,16]), C3 = C1 + C2 = C([0,14]), and C∩ = C1 ∩ C2 = C([340,16]) based on
  1. linear OA(743, 342, F7, 17) (dual of [342, 299, 18]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−2,−1,…,14}, and designed minimum distance d ≥ |I|+1 = 18 [i]
  2. linear OA(743, 342, F7, 17) (dual of [342, 299, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
  3. linear OA(749, 342, F7, 19) (dual of [342, 293, 20]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−2,−1,…,16}, and designed minimum distance d ≥ |I|+1 = 20 [i]
  4. linear OA(737, 342, F7, 15) (dual of [342, 305, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [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(751, 356, F7, 2, 19) (dual of [(356, 2), 661, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(751, 356, F7, 3, 19) (dual of [(356, 3), 1017, 20]-NRT-code) [i]
3Digital (32, 51, 356)-net over F7 [i]
4Linear OA(752, 358, F7, 19) (dual of [358, 306, 20]-code) [i]Construction X with VarÅ¡amov Bound
5Linear OOA(751, 178, F7, 2, 19) (dual of [(178, 2), 305, 20]-NRT-code) [i]OOA Folding
6Linear OOA(751, 118, F7, 3, 19) (dual of [(118, 3), 303, 20]-NRT-code) [i]