Information on Result #1302178
Linear OA(775, 235306, F7, 13) (dual of [235306, 235231, 14]-code), using construction X with Varšamov bound based on
- linear OA(774, 235304, F7, 13) (dual of [235304, 235230, 14]-code), using
- trace code [i] based on linear OA(4937, 117652, F49, 13) (dual of [117652, 117615, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(4937, 117649, F49, 13) (dual of [117649, 117612, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(4934, 117649, F49, 12) (dual of [117649, 117615, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(12) ⊂ Ce(11) [i] based on
- trace code [i] based on linear OA(4937, 117652, F49, 13) (dual of [117652, 117615, 14]-code), using
- linear OA(774, 235305, F7, 12) (dual of [235305, 235231, 13]-code), using Gilbert–Varšamov bound and bm = 774 > Vbs−1(k−1) = 1 112582 733665 983148 887713 491969 761991 730743 514477 866661 927361 [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(775, 235306, F7, 2, 13) (dual of [(235306, 2), 470537, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(775, 235306, F7, 3, 13) (dual of [(235306, 3), 705843, 14]-NRT-code) | [i] | ||
| 3 | Digital (62, 75, 235306)-net over F7 | [i] | ||
| 4 | Linear OOA(775, 117653, F7, 2, 13) (dual of [(117653, 2), 235231, 14]-NRT-code) | [i] | OOA Folding | |