Information on Result #677685

Linear OA(3119, 135, F3, 68) (dual of [135, 16, 69]-code), using construction XX applied to C([0,66]) ⊂ C([0,60]) ⊂ C([1,60]) based on
  1. linear OA(3111, 121, F3, 68) (dual of [121, 10, 69]-code), using the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,66], and minimum distance d ≥ |{−1,0,…,66}|+1 = 69 (BCH-bound) [i]
  2. linear OA(3106, 121, F3, 62) (dual of [121, 15, 63]-code), using the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,60], and minimum distance d ≥ |{−1,0,…,60}|+1 = 63 (BCH-bound) [i]
  3. linear OA(3105, 121, F3, 60) (dual of [121, 16, 61]-code), using 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]
  4. linear OA(36, 12, F3, 5) (dual of [12, 6, 6]-code), using
  5. linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-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(3119, 135, F3, 67) (dual of [135, 16, 68]-code) [i]Strength Reduction
2Linear OA(3119, 135, F3, 66) (dual of [135, 16, 67]-code) [i]
3Linear OA(3119, 135, F3, 65) (dual of [135, 16, 66]-code) [i]
4Linear OA(3119, 135, F3, 64) (dual of [135, 16, 65]-code) [i]
5Linear OA(3116, 132, F3, 65) (dual of [132, 16, 66]-code) [i]Truncation
6Linear OA(3115, 131, F3, 64) (dual of [131, 16, 65]-code) [i]
7Linear OA(3114, 130, F3, 63) (dual of [130, 16, 64]-code) [i]
8Linear OA(3111, 127, F3, 60) (dual of [127, 16, 61]-code) [i]
9Linear OA(3110, 126, F3, 59) (dual of [126, 16, 60]-code) [i]
10Linear OA(3109, 125, F3, 58) (dual of [125, 16, 59]-code) [i]
11Linear OA(3108, 124, F3, 57) (dual of [124, 16, 58]-code) [i]
12Linear OOA(3119, 45, F3, 3, 68) (dual of [(45, 3), 16, 69]-NRT-code) [i]OOA Folding
13Linear OOA(3119, 27, F3, 5, 68) (dual of [(27, 5), 16, 69]-NRT-code) [i]