Information on Result #704247

Linear OA(380, 760, F3, 18) (dual of [760, 680, 19]-code), using construction XX applied to C1 = C([724,12]), C2 = C([1,13]), C3 = C1 + C2 = C([1,12]), and C∩ = C1 ∩ C2 = C([724,13]) 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 = {−4,−3,…,12}, and designed minimum distance d ≥ |I|+1 = 18 [i]
  2. linear OA(354, 728, F3, 13) (dual of [728, 674, 14]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
  3. linear OA(373, 728, F3, 18) (dual of [728, 655, 19]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−4,−3,…,13}, and designed minimum distance d ≥ |I|+1 = 19 [i]
  4. linear OA(348, 728, F3, 12) (dual of [728, 680, 13]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(380, 757, F3, 2, 18) (dual of [(757, 2), 1434, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(380, 757, F3, 3, 18) (dual of [(757, 3), 2191, 19]-NRT-code) [i]
3Linear OOA(380, 757, F3, 4, 18) (dual of [(757, 4), 2948, 19]-NRT-code) [i]
4Linear OOA(380, 757, F3, 5, 18) (dual of [(757, 5), 3705, 19]-NRT-code) [i]
5Digital (62, 80, 757)-net over F3 [i]
6Linear OOA(380, 380, F3, 2, 18) (dual of [(380, 2), 680, 19]-NRT-code) [i]OOA Folding