Information on Result #2240426
Linear OA(486, 262175, F4, 12) (dual of [262175, 262089, 13]-code), using 1 times truncation based on linear OA(487, 262176, F4, 13) (dual of [262176, 262089, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- linear OA(482, 262144, F4, 13) (dual of [262144, 262062, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(455, 262144, F4, 9) (dual of [262144, 262089, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(488, 262177, F4, 12) (dual of [262177, 262089, 13]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(486, 197856, F4, 2, 12) (dual of [(197856, 2), 395626, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(486, 197856, F4, 3, 12) (dual of [(197856, 3), 593482, 13]-NRT-code) | [i] | ||
| 4 | Digital (74, 86, 197856)-net over F4 | [i] | ||
| 5 | Linear OA(488, 262178, F4, 12) (dual of [262178, 262090, 13]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(486, 131087, F4, 2, 12) (dual of [(131087, 2), 262088, 13]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(486, 87391, F4, 3, 12) (dual of [(87391, 3), 262087, 13]-NRT-code) | [i] | ||
| 8 | Linear OOA(486, 43695, F4, 12, 12) (dual of [(43695, 12), 524254, 13]-NRT-code) | [i] | OA Folding and Stacking | |