Information on Result #1310947
Linear OA(5136, 3193, F5, 33) (dual of [3193, 3057, 34]-code), using 58 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 6 times 0, 1, 14 times 0, 1, 32 times 0) based on linear OA(5131, 3130, F5, 33) (dual of [3130, 2999, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(31) [i] based on
- linear OA(5131, 3125, F5, 33) (dual of [3125, 2994, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(5126, 3125, F5, 32) (dual of [3125, 2999, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(50, 5, F5, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-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(5136, 3193, F5, 2, 33) (dual of [(3193, 2), 6250, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5136, 3193, F5, 3, 33) (dual of [(3193, 3), 9443, 34]-NRT-code) | [i] | ||
| 3 | Digital (103, 136, 3193)-net over F5 | [i] | ||
| 4 | Linear OOA(5136, 1596, F5, 2, 33) (dual of [(1596, 2), 3056, 34]-NRT-code) | [i] | OOA Folding | |