Information on Result #682183
Linear OA(5112, 1953155, F5, 15) (dual of [1953155, 1953043, 16]-code), using construction X applied to Ce(15) ⊂ Ce(11) based on
- linear OA(5109, 1953125, F5, 16) (dual of [1953125, 1953016, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(582, 1953125, F5, 12) (dual of [1953125, 1953043, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(53, 30, F5, 2) (dual of [30, 27, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- Hamming code H(3,5) [i]
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), 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 OOA(5112, 1316654, F5, 2, 15) (dual of [(1316654, 2), 2633196, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5112, 1316654, F5, 3, 15) (dual of [(1316654, 3), 3949850, 16]-NRT-code) | [i] | ||
| 3 | Digital (97, 112, 1316654)-net over F5 | [i] | ||
| 4 | Linear OOA(5112, 976577, F5, 2, 15) (dual of [(976577, 2), 1953042, 16]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5112, 651051, F5, 3, 15) (dual of [(651051, 3), 1953041, 16]-NRT-code) | [i] | ||
| 6 | Linear OOA(5112, 279022, F5, 15, 15) (dual of [(279022, 15), 4185218, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |