Information on Result #683011
Linear OA(542, 3137, F5, 10) (dual of [3137, 3095, 11]-code), using construction X4 applied to Ce(10) ⊂ Ce(7) based on
- linear OA(541, 3125, F5, 11) (dual of [3125, 3084, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(531, 3125, F5, 8) (dual of [3125, 3094, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(511, 12, F5, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,5)), using
- dual of repetition code with length 12 [i]
- linear OA(51, 12, F5, 1) (dual of [12, 11, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(543, 3138, F5, 10) (dual of [3138, 3095, 11]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(542, 3137, F5, 2, 10) (dual of [(3137, 2), 6232, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(542, 3137, F5, 3, 10) (dual of [(3137, 3), 9369, 11]-NRT-code) | [i] | ||
| 4 | Digital (32, 42, 3137)-net over F5 | [i] | ||
| 5 | Linear OA(543, 3139, F5, 10) (dual of [3139, 3096, 11]-code) | [i] | Construction X with Varšamov Bound | |