Information on Result #713498

Linear OA(746, 348, F7, 18) (dual of [348, 302, 19]-code), using construction XX applied to C1 = C([341,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([341,16]) 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 = {−1,0,…,15}, 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(746, 342, F7, 18) (dual of [342, 296, 19]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
  4. linear OA(740, 342, F7, 16) (dual of [342, 302, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [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(749, 365, F7, 18) (dual of [365, 316, 19]-code) [i]VarÅ¡amov–Edel Lengthening
2Linear OA(750, 387, F7, 18) (dual of [387, 337, 19]-code) [i]
3Linear OA(751, 423, F7, 18) (dual of [423, 372, 19]-code) [i]
4Linear OA(752, 470, F7, 18) (dual of [470, 418, 19]-code) [i]
5Linear OA(753, 525, F7, 18) (dual of [525, 472, 19]-code) [i]
6Linear OOA(746, 174, F7, 2, 18) (dual of [(174, 2), 302, 19]-NRT-code) [i]OOA Folding
7Linear OOA(746, 116, F7, 3, 18) (dual of [(116, 3), 302, 19]-NRT-code) [i]