Information on Result #713276

Linear OA(725, 348, F7, 10) (dual of [348, 323, 11]-code), using construction XX applied to C1 = C([341,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([341,8]) based on
  1. linear OA(722, 342, F7, 9) (dual of [342, 320, 10]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
  2. linear OA(722, 342, F7, 9) (dual of [342, 320, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
  3. 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 = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [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(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(727, 354, F7, 10) (dual of [354, 327, 11]-code) [i]VarÅ¡amov–Edel Lengthening
2Linear OA(728, 370, F7, 10) (dual of [370, 342, 11]-code) [i]
3Linear OA(729, 406, F7, 10) (dual of [406, 377, 11]-code) [i]
4Linear OA(730, 472, F7, 10) (dual of [472, 442, 11]-code) [i]
5Linear OA(731, 572, F7, 10) (dual of [572, 541, 11]-code) [i]
6Linear OOA(725, 174, F7, 2, 10) (dual of [(174, 2), 323, 11]-NRT-code) [i]OOA Folding
7Linear OOA(725, 116, F7, 3, 10) (dual of [(116, 3), 323, 11]-NRT-code) [i]