Information on Result #1315597
Linear OA(4941, 3125, F49, 17) (dual of [3125, 3084, 18]-code), using 714 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 0, 1, 16 times 0, 1, 59 times 0, 1, 185 times 0, 1, 446 times 0) based on linear OA(4933, 2403, F49, 17) (dual of [2403, 2370, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(4933, 2401, F49, 17) (dual of [2401, 2368, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(4931, 2401, F49, 16) (dual of [2401, 2370, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 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(4941, 3125, F49, 2, 17) (dual of [(3125, 2), 6209, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4941, 3125, F49, 3, 17) (dual of [(3125, 3), 9334, 18]-NRT-code) | [i] | ||
| 3 | Digital (24, 41, 3125)-net over F49 | [i] | ||
| 4 | Linear OOA(4941, 1562, F49, 2, 17) (dual of [(1562, 2), 3083, 18]-NRT-code) | [i] | OOA Folding | |