Information on Result #1301961
Linear OA(727, 235306, F7, 5) (dual of [235306, 235279, 6]-code), using construction X with Varšamov bound based on
- linear OA(726, 235304, F7, 5) (dual of [235304, 235278, 6]-code), using
- trace code [i] based on linear OA(4913, 117652, F49, 5) (dual of [117652, 117639, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(4913, 117649, F49, 5) (dual of [117649, 117636, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(4910, 117649, F49, 4) (dual of [117649, 117639, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(490, 3, F49, 0) (dual of [3, 3, 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
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- trace code [i] based on linear OA(4913, 117652, F49, 5) (dual of [117652, 117639, 6]-code), using
- linear OA(726, 235305, F7, 4) (dual of [235305, 235279, 5]-code), using Gilbert–Varšamov bound and bm = 726 > Vbs−1(k−1) = 469014 010626 081505 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 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(727, 235306, F7, 2, 5) (dual of [(235306, 2), 470585, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(727, 235306, F7, 3, 5) (dual of [(235306, 3), 705891, 6]-NRT-code) | [i] | ||
| 3 | Digital (22, 27, 235306)-net over F7 | [i] | ||
| 4 | Linear OOA(727, 117653, F7, 2, 5) (dual of [(117653, 2), 235279, 6]-NRT-code) | [i] | OOA Folding | |