Information on Result #1302536
Linear OA(869, 262160, F8, 13) (dual of [262160, 262091, 14]-code), using construction X with Varšamov bound based on
- linear OA(868, 262158, F8, 13) (dual of [262158, 262090, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(867, 262144, F8, 13) (dual of [262144, 262077, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(855, 262144, F8, 11) (dual of [262144, 262089, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(813, 14, F8, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,8)), using
- dual of repetition code with length 14 [i]
- linear OA(81, 14, F8, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(868, 262159, F8, 12) (dual of [262159, 262091, 13]-code), using Gilbert–Varšamov bound and bm = 868 > Vbs−1(k−1) = 19 908038 744160 248355 508131 320325 736876 736888 956641 626385 543506 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 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(869, 262160, F8, 2, 13) (dual of [(262160, 2), 524251, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(869, 262160, F8, 3, 13) (dual of [(262160, 3), 786411, 14]-NRT-code) | [i] | ||
| 3 | Digital (56, 69, 262160)-net over F8 | [i] | ||
| 4 | Linear OOA(869, 131080, F8, 2, 13) (dual of [(131080, 2), 262091, 14]-NRT-code) | [i] | OOA Folding | |