Information on Result #704325

Linear OA(375, 742, F3, 19) (dual of [742, 667, 20]-code), using construction XX applied to C1 = C([351,367]), C2 = C([349,365]), C3 = C1 + C2 = C([351,365]), and C∩ = C1 ∩ C2 = C([349,367]) based on
  1. linear OA(367, 728, F3, 17) (dual of [728, 661, 18]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {351,352,…,367}, and designed minimum distance d ≥ |I|+1 = 18 [i]
  2. linear OA(367, 728, F3, 17) (dual of [728, 661, 18]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {349,350,…,365}, and designed minimum distance d ≥ |I|+1 = 18 [i]
  3. linear OA(373, 728, F3, 19) (dual of [728, 655, 20]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {349,350,…,367}, and designed minimum distance d ≥ |I|+1 = 20 [i]
  4. linear OA(361, 728, F3, 15) (dual of [728, 667, 16]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {351,352,…,365}, and designed minimum distance d ≥ |I|+1 = 16 [i]
  5. linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
  6. linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-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(376, 743, F3, 19) (dual of [743, 667, 20]-code) [i]Code Embedding in Larger Space
2Linear OA(383, 765, F3, 19) (dual of [765, 682, 20]-code) [i]VarÅ¡amov–Edel Lengthening
3Linear OOA(375, 371, F3, 2, 19) (dual of [(371, 2), 667, 20]-NRT-code) [i]OOA Folding
4Linear OOA(375, 247, F3, 3, 19) (dual of [(247, 3), 666, 20]-NRT-code) [i]
5Linear OOA(375, 185, F3, 4, 19) (dual of [(185, 4), 665, 20]-NRT-code) [i]
6Linear OOA(375, 148, F3, 5, 19) (dual of [(148, 5), 665, 20]-NRT-code) [i]