Information on Result #713175

Linear OA(710, 348, F7, 4) (dual of [348, 338, 5]-code), using construction XX applied to C1 = C([341,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([341,2]) based on
  1. linear OA(77, 342, F7, 3) (dual of [342, 335, 4]-code or 342-cap in PG(6,7)), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [i]
  2. linear OA(77, 342, F7, 3) (dual of [342, 335, 4]-code or 342-cap in PG(6,7)), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
  3. linear OA(710, 342, F7, 4) (dual of [342, 332, 5]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
  4. linear OA(74, 342, F7, 2) (dual of [342, 338, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [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(710, 348, F7, 2, 4) (dual of [(348, 2), 686, 5]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(710, 348, F7, 3, 4) (dual of [(348, 3), 1034, 5]-NRT-code) [i]
3Linear OOA(710, 174, F7, 2, 4) (dual of [(174, 2), 338, 5]-NRT-code) [i]OOA Folding
4Linear OOA(710, 174, F7, 3, 4) (dual of [(174, 3), 512, 5]-NRT-code) [i]OA Folding and Stacking