Information on Result #1310924
Linear OA(5131, 3156, F5, 32) (dual of [3156, 3025, 33]-code), using 21 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 4 times 0, 1, 12 times 0) based on linear OA(5126, 3130, F5, 32) (dual of [3130, 3004, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- 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(5121, 3125, F5, 31) (dual of [3125, 3004, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(5131, 3156, F5, 2, 32) (dual of [(3156, 2), 6181, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5131, 3156, F5, 3, 32) (dual of [(3156, 3), 9337, 33]-NRT-code) | [i] | ||
| 3 | Digital (99, 131, 3156)-net over F5 | [i] | ||
| 4 | Linear OOA(5131, 1578, F5, 2, 32) (dual of [(1578, 2), 3025, 33]-NRT-code) | [i] | OOA Folding | |