Information on Result #1324346
Linear OA(8112, 2097215, F8, 17) (dual of [2097215, 2097103, 18]-code), using construction X with Varšamov bound based on
- linear OA(8111, 2097213, F8, 17) (dual of [2097213, 2097102, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(8) [i] based on
- linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(850, 2097152, F8, 9) (dual of [2097152, 2097102, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(812, 61, F8, 7) (dual of [61, 49, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(812, 73, F8, 7) (dual of [73, 61, 8]-code), using
- a “DaH†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(812, 73, F8, 7) (dual of [73, 61, 8]-code), using
- construction X applied to Ce(16) ⊂ Ce(8) [i] based on
- linear OA(8111, 2097214, F8, 16) (dual of [2097214, 2097103, 17]-code), using Gilbert–Varšamov bound and bm = 8111 > Vbs−1(k−1) = 242430 806293 718027 037072 910003 956741 500488 002409 053473 017324 342118 693973 857452 895419 567201 562768 [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(8112, 2097215, F8, 2, 17) (dual of [(2097215, 2), 4194318, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8112, 2097215, F8, 3, 17) (dual of [(2097215, 3), 6291533, 18]-NRT-code) | [i] | ||
| 3 | Digital (95, 112, 2097215)-net over F8 | [i] | ||