Information on Result #613586
Linear OA(537, 1953125, F5, 6) (dual of [1953125, 1953088, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6
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(536, 1953124, F5, 5) (dual of [1953124, 1953088, 6]-code) | [i] | Truncation | |
| 2 | Linear OA(540, 1953131, F5, 6) (dual of [1953131, 1953091, 7]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OOA(537, 1080742, F5, 2, 6) (dual of [(1080742, 2), 2161447, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(537, 1080742, F5, 3, 6) (dual of [(1080742, 3), 3242189, 7]-NRT-code) | [i] | ||
| 5 | Digital (31, 37, 1080742)-net over F5 | [i] | ||
| 6 | Linear OA(546, 1953134, F5, 7) (dual of [1953134, 1953088, 8]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 7 | Linear OA(538, 1953135, F5, 6) (dual of [1953135, 1953097, 7]-code) | [i] | ✔ | |
| 8 | Linear OA(556, 1953144, F5, 8) (dual of [1953144, 1953088, 9]-code) | [i] | ✔ | |
| 9 | Linear OA(540, 1953146, F5, 6) (dual of [1953146, 1953106, 7]-code) | [i] | ✔ | |
| 10 | Linear OA(567, 1953155, F5, 9) (dual of [1953155, 1953088, 10]-code) | [i] | ✔ | |
| 11 | Linear OA(578, 1953166, F5, 10) (dual of [1953166, 1953088, 11]-code) | [i] | ✔ | |
| 12 | Linear OA(580, 1953168, F5, 11) (dual of [1953168, 1953088, 12]-code) | [i] | ✔ | |
| 13 | Linear OA(547, 1953136, F5, 7) (dual of [1953136, 1953089, 8]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |
| 14 | Linear OA(538, 1953136, F5, 6) (dual of [1953136, 1953098, 7]-code) | [i] | ✔ | |
| 15 | Linear OA(556, 1953145, F5, 8) (dual of [1953145, 1953089, 9]-code) | [i] | ✔ | |
| 16 | Linear OOA(537, 976562, F5, 2, 6) (dual of [(976562, 2), 1953087, 7]-NRT-code) | [i] | OOA Folding | |
| 17 | Linear OOA(537, 651041, F5, 3, 6) (dual of [(651041, 3), 1953086, 7]-NRT-code) | [i] | ||
| 18 | Linear OOA(537, 651041, F5, 6, 6) (dual of [(651041, 6), 3906209, 7]-NRT-code) | [i] | OA Folding and Stacking | |