Information on Result #680019
Linear OA(439, 4105, F4, 9) (dual of [4105, 4066, 10]-code), using construction XX applied to Ce(8) ⊂ Ce(6) ⊂ Ce(5) based on
- linear OA(437, 4096, F4, 9) (dual of [4096, 4059, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(431, 4096, F4, 7) (dual of [4096, 4065, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(425, 4096, F4, 6) (dual of [4096, 4071, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(41, 8, F4, 1) (dual of [8, 7, 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, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(439, 2085, F4, 2, 9) (dual of [(2085, 2), 4131, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(439, 2085, F4, 3, 9) (dual of [(2085, 3), 6216, 10]-NRT-code) | [i] | ||
| 3 | Digital (30, 39, 2085)-net over F4 | [i] | ||
| 4 | Linear OOA(439, 2052, F4, 2, 9) (dual of [(2052, 2), 4065, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(439, 1368, F4, 3, 9) (dual of [(1368, 3), 4065, 10]-NRT-code) | [i] | ||