Information on Result #1324316
Linear OA(5135, 15676, F5, 26) (dual of [15676, 15541, 27]-code), using construction X with Varšamov bound based on
- linear OA(5134, 15674, F5, 26) (dual of [15674, 15540, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(585, 15625, F5, 18) (dual of [15625, 15540, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(513, 49, F5, 7) (dual of [49, 36, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(513, 52, F5, 7) (dual of [52, 39, 8]-code), using
- a “LX†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(513, 52, F5, 7) (dual of [52, 39, 8]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- linear OA(5134, 15675, F5, 25) (dual of [15675, 15541, 26]-code), using Gilbert–Varšamov bound and bm = 5134 > Vbs−1(k−1) = 21 555874 235072 028556 907080 021809 290092 783795 512952 238809 345112 329278 057487 273207 155042 055225 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 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(5135, 15676, F5, 2, 26) (dual of [(15676, 2), 31217, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5135, 15676, F5, 3, 26) (dual of [(15676, 3), 46893, 27]-NRT-code) | [i] | ||
| 3 | Digital (109, 135, 15676)-net over F5 | [i] | ||
| 4 | Linear OOA(5135, 7838, F5, 2, 26) (dual of [(7838, 2), 15541, 27]-NRT-code) | [i] | OOA Folding | |