Information on Result #2237971
Linear OA(459, 262175, F4, 8) (dual of [262175, 262116, 9]-code), using 1 times truncation based on linear OA(460, 262176, F4, 9) (dual of [262176, 262116, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(4) [i] based on
- 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(428, 262144, F4, 5) (dual of [262144, 262116, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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 OOA(459, 262175, F4, 2, 8) (dual of [(262175, 2), 524291, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(459, 262175, F4, 3, 8) (dual of [(262175, 3), 786466, 9]-NRT-code) | [i] | ||
| 3 | Digital (51, 59, 262175)-net over F4 | [i] | ||
| 4 | Linear OOA(459, 131087, F4, 2, 8) (dual of [(131087, 2), 262115, 9]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(459, 87391, F4, 3, 8) (dual of [(87391, 3), 262114, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(459, 65543, F4, 8, 8) (dual of [(65543, 8), 524285, 9]-NRT-code) | [i] | OA Folding and Stacking | |