Information on Result #684055
Linear OA(514, 129, F5, 6) (dual of [129, 115, 7]-code), using construction X applied to Ce(5) ⊂ Ce(3) based on
- linear OA(513, 125, F5, 6) (dual of [125, 112, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(510, 125, F5, 4) (dual of [125, 115, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(51, 4, F5, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(514, 102, F5, 2, 6) (dual of [(102, 2), 190, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(514, 102, F5, 3, 6) (dual of [(102, 3), 292, 7]-NRT-code) | [i] | ||
| 3 | Digital (8, 14, 102)-net over F5 | [i] | ||
| 4 | Linear OA(515, 132, F5, 6) (dual of [132, 117, 7]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OOA(514, 64, F5, 2, 6) (dual of [(64, 2), 114, 7]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(514, 43, F5, 3, 6) (dual of [(43, 3), 115, 7]-NRT-code) | [i] | ||