Information on Result #1302113
Linear OA(763, 235306, F7, 11) (dual of [235306, 235243, 12]-code), using construction X with Varšamov bound based on
- linear OA(762, 235304, F7, 11) (dual of [235304, 235242, 12]-code), using
- trace code [i] based on linear OA(4931, 117652, F49, 11) (dual of [117652, 117621, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(4931, 117649, F49, 11) (dual of [117649, 117618, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(4928, 117649, F49, 10) (dual of [117649, 117621, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(10) ⊂ Ce(9) [i] based on
- trace code [i] based on linear OA(4931, 117652, F49, 11) (dual of [117652, 117621, 12]-code), using
- linear OA(762, 235305, F7, 10) (dual of [235305, 235243, 11]-code), using Gilbert–Varšamov bound and bm = 762 > Vbs−1(k−1) = 61 404236 191426 512334 124678 402318 203522 746040 359361 [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(763, 235306, F7, 2, 11) (dual of [(235306, 2), 470549, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(763, 235306, F7, 3, 11) (dual of [(235306, 3), 705855, 12]-NRT-code) | [i] | ||
| 3 | Digital (52, 63, 235306)-net over F7 | [i] | ||
| 4 | Linear OOA(763, 117653, F7, 2, 11) (dual of [(117653, 2), 235243, 12]-NRT-code) | [i] | OOA Folding | |