Information on Result #676681

Linear OA(3117, 749, F3, 29) (dual of [749, 632, 30]-code), using construction X applied to Ce(28) ⊂ Ce(24) based on
  1. linear OA(3112, 729, F3, 29) (dual of [729, 617, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
  2. linear OA(397, 729, F3, 25) (dual of [729, 632, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
  3. linear OA(35, 20, F3, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), 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 OA(3118, 750, F3, 29) (dual of [750, 632, 30]-code) [i]Code Embedding in Larger Space
2Linear OA(3119, 751, F3, 29) (dual of [751, 632, 30]-code) [i]
3Linear OOA(3117, 589, F3, 2, 29) (dual of [(589, 2), 1061, 30]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(3117, 589, F3, 3, 29) (dual of [(589, 3), 1650, 30]-NRT-code) [i]
5Linear OOA(3117, 589, F3, 4, 29) (dual of [(589, 4), 2239, 30]-NRT-code) [i]
6Linear OOA(3117, 589, F3, 5, 29) (dual of [(589, 5), 2828, 30]-NRT-code) [i]
7Digital (88, 117, 589)-net over F3 [i]
8Linear OA(3119, 752, F3, 29) (dual of [752, 633, 30]-code) [i]Construction X with VarÅ¡amov Bound
9Linear OOA(3117, 374, F3, 2, 29) (dual of [(374, 2), 631, 30]-NRT-code) [i]OOA Folding
10Linear OOA(3117, 249, F3, 3, 29) (dual of [(249, 3), 630, 30]-NRT-code) [i]
11Linear OOA(3117, 187, F3, 4, 29) (dual of [(187, 4), 631, 30]-NRT-code) [i]