Information on Result #677647

Linear OA(3117, 133, F3, 67) (dual of [133, 16, 68]-code), using construction X applied to Ce(66) ⊂ Ce(60) based on
  1. linear OA(3111, 122, F3, 67) (dual of [122, 11, 68]-code), using an extension Ce(66) of the narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [1,66], and designed minimum distance d ≥ |I|+1 = 67 [i]
  2. linear OA(3106, 122, F3, 61) (dual of [122, 16, 62]-code), using an extension Ce(60) of the narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [1,60], and designed minimum distance d ≥ |I|+1 = 61 [i]
  3. linear OA(36, 11, F3, 5) (dual of [11, 5, 6]-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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(3117, 133, F3, 66) (dual of [133, 16, 67]-code) [i]Strength Reduction
2Linear OA(3117, 133, F3, 65) (dual of [133, 16, 66]-code) [i]
3Linear OA(3117, 133, F3, 64) (dual of [133, 16, 65]-code) [i]
4Linear OA(3117, 133, F3, 63) (dual of [133, 16, 64]-code) [i]
5Linear OA(3117, 133, F3, 62) (dual of [133, 16, 63]-code) [i]
6Linear OA(3120, 136, F3, 67) (dual of [136, 16, 68]-code) [i]Code Embedding in Larger Space
7Linear OA(3136, 157, F3, 67) (dual of [157, 21, 68]-code) [i]Construction X with VarÅ¡amov Bound
8Linear OOA(3117, 66, F3, 2, 67) (dual of [(66, 2), 15, 68]-NRT-code) [i]OOA Folding
9Linear OOA(3117, 44, F3, 3, 67) (dual of [(44, 3), 15, 68]-NRT-code) [i]