Information on Result #682635
Linear OA(5122, 15632, F5, 26) (dual of [15632, 15510, 27]-code), using construction X applied to Ce(25) ⊂ Ce(23) 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(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(51, 7, F5, 1) (dual of [7, 6, 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(5121, 15631, F5, 25) (dual of [15631, 15510, 26]-code) | [i] | Truncation | |
| 2 | Linear OOA(5122, 8173, F5, 2, 26) (dual of [(8173, 2), 16224, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(5122, 8173, F5, 3, 26) (dual of [(8173, 3), 24397, 27]-NRT-code) | [i] | ||
| 4 | Digital (96, 122, 8173)-net over F5 | [i] | ||
| 5 | Linear OOA(5122, 7816, F5, 2, 26) (dual of [(7816, 2), 15510, 27]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(5122, 5210, F5, 3, 26) (dual of [(5210, 3), 15508, 27]-NRT-code) | [i] | ||
| 7 | Linear OOA(5122, 1202, F5, 26, 26) (dual of [(1202, 26), 31130, 27]-NRT-code) | [i] | OA Folding and Stacking | |