Information on Result #713341

Linear OA(734, 348, F7, 13) (dual of [348, 314, 14]-code), using construction XX applied to C1 = C([341,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([341,11]) based on
  1. 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]
  2. linear OA(731, 342, F7, 12) (dual of [342, 311, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
  3. linear OA(734, 342, F7, 13) (dual of [342, 308, 14]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
  4. 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]
  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(737, 380, F7, 13) (dual of [380, 343, 14]-code) [i]VarÅ¡amov–Edel Lengthening
2Linear OA(738, 429, F7, 13) (dual of [429, 391, 14]-code) [i]
3Linear OA(739, 499, F7, 13) (dual of [499, 460, 14]-code) [i]
4Linear OA(740, 585, F7, 13) (dual of [585, 545, 14]-code) [i]
5Linear OOA(734, 174, F7, 2, 13) (dual of [(174, 2), 314, 14]-NRT-code) [i]OOA Folding
6Linear OOA(734, 116, F7, 3, 13) (dual of [(116, 3), 314, 14]-NRT-code) [i]