Information on Result #1310321
Linear OA(523, 3135, F5, 6) (dual of [3135, 3112, 7]-code), using 2 step Varšamov–Edel lengthening with (ri) = (1, 0) based on linear OA(522, 3132, F5, 6) (dual of [3132, 3110, 7]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(521, 3125, F5, 6) (dual of [3125, 3104, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(516, 3125, F5, 4) (dual of [3125, 3109, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(56, 7, F5, 6) (dual of [7, 1, 7]-code or 7-arc in PG(5,5)), using
- dual of repetition code with length 7 [i]
- linear OA(51, 7, F5, 1) (dual of [7, 6, 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: 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(523, 3135, F5, 2, 6) (dual of [(3135, 2), 6247, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(523, 3135, F5, 3, 6) (dual of [(3135, 3), 9382, 7]-NRT-code) | [i] | ||
| 3 | Digital (17, 23, 3135)-net over F5 | [i] | ||