Information on Result #1307548
Linear OA(443, 287, F4, 13) (dual of [287, 244, 14]-code), using 18 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 4 times 0, 1, 10 times 0) based on linear OA(439, 265, F4, 13) (dual of [265, 226, 14]-code), using
- construction XX applied to C1 = C([79,89]), C2 = C([77,87]), C3 = C1 + C2 = C([79,87]), and C∩ = C1 ∩ C2 = C([77,89]) [i] based on
- linear OA(433, 255, F4, 11) (dual of [255, 222, 12]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {79,80,…,89}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(433, 255, F4, 11) (dual of [255, 222, 12]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {77,78,…,87}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(437, 255, F4, 13) (dual of [255, 218, 14]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {77,78,…,89}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(429, 255, F4, 9) (dual of [255, 226, 10]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {79,80,…,87}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(41, 5, F4, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(41, 5, F4, 1) (dual of [5, 4, 2]-code) (see above)
Mode: 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 OOA(443, 287, F4, 2, 13) (dual of [(287, 2), 531, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(443, 287, F4, 3, 13) (dual of [(287, 3), 818, 14]-NRT-code) | [i] | ||
| 3 | Digital (30, 43, 287)-net over F4 | [i] | ||