Information on Result #614177
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
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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(5105, 125, F5, 67) (dual of [125, 20, 68]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(5105, 125, F5, 66) (dual of [125, 20, 67]-code) | [i] | ||
| 3 | Linear OA(5106, 126, F5, 68) (dual of [126, 20, 69]-code) | [i] | Code Embedding in Larger Space | |
| 4 | Linear OA(5103, 123, F5, 66) (dual of [123, 20, 67]-code) | [i] | Truncation | |
| 5 | Linear OA(5102, 122, F5, 65) (dual of [122, 20, 66]-code) | [i] | ||
| 6 | Linear OA(5101, 121, F5, 64) (dual of [121, 20, 65]-code) | [i] | ||
| 7 | Linear OA(5108, 128, F5, 69) (dual of [128, 20, 70]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 8 | Linear OA(5108, 131, F5, 68) (dual of [131, 23, 69]-code) | [i] | ✔ | |
| 9 | Linear OA(5112, 132, F5, 70) (dual of [132, 20, 71]-code) | [i] | ✔ | |
| 10 | Linear OA(5116, 136, F5, 73) (dual of [136, 20, 74]-code) | [i] | ✔ | |
| 11 | Linear OA(5110, 136, F5, 68) (dual of [136, 26, 69]-code) | [i] | ✔ | |
| 12 | Linear OA(5107, 131, F5, 66) (dual of [131, 24, 67]-code) | [i] | ✔ | |
| 13 | Linear OA(5121, 141, F5, 74) (dual of [141, 20, 75]-code) | [i] | ✔ | |
| 14 | Linear OA(5112, 139, F5, 68) (dual of [139, 27, 69]-code) | [i] | ✔ | |
| 15 | Linear OA(5109, 136, F5, 66) (dual of [136, 27, 67]-code) | [i] | ✔ | |
| 16 | Linear OA(5143, 163, F5, 86) (dual of [163, 20, 87]-code) | [i] | ✔ | |
| 17 | Linear OA(5137, 158, F5, 80) (dual of [158, 21, 81]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 18 | Linear OA(5138, 161, F5, 80) (dual of [161, 23, 81]-code) | [i] | ✔ | |
| 19 | Linear OA(5137, 159, F5, 80) (dual of [159, 22, 81]-code) | [i] | ✔ | |
| 20 | Linear OA(5136, 157, F5, 80) (dual of [157, 21, 81]-code) | [i] | ✔ | |
| 21 | Linear OA(5126, 148, F5, 74) (dual of [148, 22, 75]-code) | [i] | ✔ | |
| 22 | Linear OA(5125, 146, F5, 74) (dual of [146, 21, 75]-code) | [i] | ✔ | |
| 23 | Linear OA(5114, 132, F5, 72) (dual of [132, 18, 73]-code) | [i] | ✔ | |
| 24 | Linear OA(5122, 144, F5, 73) (dual of [144, 22, 74]-code) | [i] | ✔ | |
| 25 | Linear OA(5120, 142, F5, 72) (dual of [142, 22, 73]-code) | [i] | ✔ | |
| 26 | Linear OA(5117, 139, F5, 70) (dual of [139, 22, 71]-code) | [i] | ✔ | |
| 27 | Linear OA(5119, 140, F5, 72) (dual of [140, 21, 73]-code) | [i] | ✔ | |
| 28 | Linear OA(5112, 133, F5, 69) (dual of [133, 21, 70]-code) | [i] | ✔ | |
| 29 | Linear OA(5108, 132, F5, 67) (dual of [132, 24, 68]-code) | [i] | ✔ | |
| 30 | Linear OA(5110, 137, F5, 67) (dual of [137, 27, 68]-code) | [i] | ✔ | |
| 31 | Linear OA(5111, 138, F5, 68) (dual of [138, 27, 69]-code) | [i] | ✔ | |