Information on Result #713463

Linear OA(743, 348, F7, 17) (dual of [348, 305, 18]-code), using construction XX applied to C1 = C([341,14]), C2 = C([0,15]), C3 = C1 + C2 = C([0,14]), and C∩ = C1 ∩ C2 = C([341,15]) based on
  1. linear OA(740, 342, F7, 16) (dual of [342, 302, 17]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,14}, and designed minimum distance d ≥ |I|+1 = 17 [i]
  2. 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]
  3. 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]
  4. linear OA(737, 342, F7, 15) (dual of [342, 305, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [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(746, 360, F7, 17) (dual of [360, 314, 18]-code) [i]VarÅ¡amov–Edel Lengthening
2Linear OA(747, 376, F7, 17) (dual of [376, 329, 18]-code) [i]
3Linear OA(748, 406, F7, 17) (dual of [406, 358, 18]-code) [i]
4Linear OA(749, 450, F7, 17) (dual of [450, 401, 18]-code) [i]
5Linear OOA(743, 174, F7, 2, 17) (dual of [(174, 2), 305, 18]-NRT-code) [i]OOA Folding
6Linear OOA(743, 116, F7, 3, 17) (dual of [(116, 3), 305, 18]-NRT-code) [i]