Information on Result #698232
Linear OA(497, 2403, F49, 4) (dual of [2403, 2396, 5]-code), using construction X applied to Ce(3) ⊂ Ce(2) based on
- linear OA(497, 2401, F49, 4) (dual of [2401, 2394, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(495, 2401, F49, 3) (dual of [2401, 2396, 4]-code or 2401-cap in PG(4,49)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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: 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(714, 4806, F7, 4) (dual of [4806, 4792, 5]-code) | [i] | Trace Code | |
| 2 | Linear OA(4932, 120055, F49, 9) (dual of [120055, 120023, 10]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(4940, 5767208, F49, 9) (dual of [5767208, 5767168, 10]-code) | [i] | ||
| 4 | Linear OA(4912, 117747, F49, 4) (dual of [117747, 117735, 5]-code) | [i] | Generalized (u, u+v)-Construction | |
| 5 | Linear OOA(497, 2403, F49, 2, 4) (dual of [(2403, 2), 4799, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(497, 2403, F49, 3, 4) (dual of [(2403, 3), 7202, 5]-NRT-code) | [i] | ||
| 7 | Linear OA(498, 2501, F49, 4) (dual of [2501, 2493, 5]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OOA(497, 1201, F49, 2, 4) (dual of [(1201, 2), 2395, 5]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(497, 1201, F49, 3, 4) (dual of [(1201, 3), 3596, 5]-NRT-code) | [i] | OA Folding and Stacking | |