Information on Result #678518
Linear OA(485, 262167, F4, 12) (dual of [262167, 262082, 13]-code), using construction XX applied to Ce(12) ⊂ Ce(9) ⊂ Ce(8) 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(464, 262144, F4, 10) (dual of [262144, 262080, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(41, 21, F4, 1) (dual of [21, 20, 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(40, 2, F4, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(485, 172243, F4, 2, 12) (dual of [(172243, 2), 344401, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(485, 172243, F4, 3, 12) (dual of [(172243, 3), 516644, 13]-NRT-code) | [i] | ||
| 3 | Digital (73, 85, 172243)-net over F4 | [i] | ||
| 4 | Linear OOA(485, 87389, F4, 3, 12) (dual of [(87389, 3), 262082, 13]-NRT-code) | [i] | OOA Folding | |