Information on Result #682375
Linear OA(569, 390654, F5, 10) (dual of [390654, 390585, 11]-code), using construction XX applied to Ce(10) ⊂ Ce(6) ⊂ Ce(5) based on
- linear OA(565, 390625, F5, 11) (dual of [390625, 390560, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(541, 390625, F5, 7) (dual of [390625, 390584, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(533, 390625, F5, 6) (dual of [390625, 390592, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(53, 28, F5, 2) (dual of [28, 25, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- Hamming code H(3,5) [i]
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- linear OA(50, 1, F5, 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(569, 390654, F5, 2, 10) (dual of [(390654, 2), 781239, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(569, 390654, F5, 3, 10) (dual of [(390654, 3), 1171893, 11]-NRT-code) | [i] | ||
| 3 | Digital (59, 69, 390654)-net over F5 | [i] | ||
| 4 | Linear OOA(569, 195327, F5, 2, 10) (dual of [(195327, 2), 390585, 11]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(569, 130218, F5, 3, 10) (dual of [(130218, 3), 390585, 11]-NRT-code) | [i] | ||