Information on Result #704312

Linear OA(392, 760, F3, 21) (dual of [760, 668, 22]-code), using construction XX applied to C1 = C([724,15]), C2 = C([1,16]), C3 = C1 + C2 = C([1,15]), and C∩ = C1 ∩ C2 = C([724,16]) based on
  1. linear OA(379, 728, F3, 20) (dual of [728, 649, 21]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,15}, and designed minimum distance d ≥ |I|+1 = 21 [i]
  2. linear OA(366, 728, F3, 16) (dual of [728, 662, 17]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  3. linear OA(385, 728, F3, 21) (dual of [728, 643, 22]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,16}, and designed minimum distance d ≥ |I|+1 = 22 [i]
  4. linear OA(360, 728, F3, 15) (dual of [728, 668, 16]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
  5. linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using
    • the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
  6. linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code), using

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 OOA(392, 747, F3, 2, 21) (dual of [(747, 2), 1402, 22]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(392, 747, F3, 3, 21) (dual of [(747, 3), 2149, 22]-NRT-code) [i]
3Linear OOA(392, 747, F3, 4, 21) (dual of [(747, 4), 2896, 22]-NRT-code) [i]
4Linear OOA(392, 747, F3, 5, 21) (dual of [(747, 5), 3643, 22]-NRT-code) [i]
5Digital (71, 92, 747)-net over F3 [i]
6Linear OOA(392, 380, F3, 2, 21) (dual of [(380, 2), 668, 22]-NRT-code) [i]OOA Folding