Information on Result #684120
Linear OA(5112, 139, F5, 68) (dual of [139, 27, 69]-code), using construction X applied to Ce(67) ⊂ Ce(61) based on
- linear OA(5105, 125, F5, 68) (dual of [125, 20, 69]-code), using an extension Ce(67) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,67], and designed minimum distance d ≥ |I|+1 = 68 [i]
- linear OA(598, 125, F5, 62) (dual of [125, 27, 63]-code), using an extension Ce(61) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,61], and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(57, 14, F5, 5) (dual of [14, 7, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 21, F5, 5) (dual of [21, 14, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(5112, 139, F5, 67) (dual of [139, 27, 68]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(5112, 139, F5, 66) (dual of [139, 27, 67]-code) | [i] | ||
| 3 | Linear OA(5112, 139, F5, 65) (dual of [139, 27, 66]-code) | [i] | ||
| 4 | Linear OA(5112, 139, F5, 64) (dual of [139, 27, 65]-code) | [i] | ||
| 5 | Linear OA(5108, 135, F5, 64) (dual of [135, 27, 65]-code) | [i] | Truncation | |
| 6 | Linear OA(5107, 134, F5, 63) (dual of [134, 27, 64]-code) | [i] | ||
| 7 | Linear OA(5105, 132, F5, 61) (dual of [132, 27, 62]-code) | [i] | ||
| 8 | Linear OA(5104, 131, F5, 60) (dual of [131, 27, 61]-code) | [i] | ||
| 9 | Linear OA(5102, 129, F5, 58) (dual of [129, 27, 59]-code) | [i] | ||
| 10 | Linear OA(5101, 128, F5, 57) (dual of [128, 27, 58]-code) | [i] | ||
| 11 | Linear OA(5100, 127, F5, 56) (dual of [127, 27, 57]-code) | [i] | ||
| 12 | Linear OA(596, 123, F5, 52) (dual of [123, 27, 53]-code) | [i] | ||
| 13 | Linear OA(595, 122, F5, 51) (dual of [122, 27, 52]-code) | [i] | ||
| 14 | Linear OA(594, 121, F5, 50) (dual of [121, 27, 51]-code) | [i] | ||
| 15 | Linear OA(593, 120, F5, 49) (dual of [120, 27, 50]-code) | [i] | ||
| 16 | Linear OA(5118, 147, F5, 68) (dual of [147, 29, 69]-code) | [i] | Construction X with Varšamov Bound | |
| 17 | Linear OA(5118, 148, F5, 67) (dual of [148, 30, 68]-code) | [i] | ||