Information on Result #713315

Linear OA(731, 348, F7, 12) (dual of [348, 317, 13]-code), using construction XX applied to C1 = C([341,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([341,10]) based on
  1. linear OA(728, 342, F7, 11) (dual of [342, 314, 12]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
  2. linear OA(728, 342, F7, 11) (dual of [342, 314, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [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 = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
  4. 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]
  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 OA(734, 375, F7, 12) (dual of [375, 341, 13]-code) [i]VarÅ¡amov–Edel Lengthening
2Linear OA(735, 419, F7, 12) (dual of [419, 384, 13]-code) [i]
3Linear OA(736, 487, F7, 12) (dual of [487, 451, 13]-code) [i]
4Linear OA(737, 576, F7, 12) (dual of [576, 539, 13]-code) [i]
5Linear OOA(731, 174, F7, 2, 12) (dual of [(174, 2), 317, 13]-NRT-code) [i]OOA Folding
6Linear OOA(731, 116, F7, 3, 12) (dual of [(116, 3), 317, 13]-NRT-code) [i]