Information on Result #1302347
Linear OA(7105, 235306, F7, 18) (dual of [235306, 235201, 19]-code), using construction X with Varšamov bound based on
- linear OA(7104, 235304, F7, 18) (dual of [235304, 235200, 19]-code), using
- trace code [i] based on linear OA(4952, 117652, F49, 18) (dual of [117652, 117600, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(4952, 117649, F49, 18) (dual of [117649, 117597, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(4949, 117649, F49, 17) (dual of [117649, 117600, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(17) ⊂ Ce(16) [i] based on
- trace code [i] based on linear OA(4952, 117652, F49, 18) (dual of [117652, 117600, 19]-code), using
- linear OA(7104, 235305, F7, 17) (dual of [235305, 235201, 18]-code), using Gilbert–Varšamov bound and bm = 7104 > Vbs−1(k−1) = 11 902900 623162 456076 864330 667369 564827 303587 618199 301069 651924 415907 728805 908142 610881 [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(7105, 235306, F7, 2, 18) (dual of [(235306, 2), 470507, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(7105, 235306, F7, 3, 18) (dual of [(235306, 3), 705813, 19]-NRT-code) | [i] | ||
| 3 | Digital (87, 105, 235306)-net over F7 | [i] | ||
| 4 | Linear OOA(7105, 117653, F7, 2, 18) (dual of [(117653, 2), 235201, 19]-NRT-code) | [i] | OOA Folding | |