Information on Result #686252
Linear OA(822, 2097159, F8, 4) (dual of [2097159, 2097137, 5]-code), using construction X applied to Ce(3) ⊂ Ce(2) based on
- linear OA(822, 2097152, F8, 4) (dual of [2097152, 2097130, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(815, 2097152, F8, 3) (dual of [2097152, 2097137, 4]-code or 2097152-cap in PG(14,8)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(80, 7, F8, 0) (dual of [7, 7, 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: Constructive and 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(822, 2097159, F8, 2, 4) (dual of [(2097159, 2), 4194296, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(822, 2097159, F8, 3, 4) (dual of [(2097159, 3), 6291455, 5]-NRT-code) | [i] | ||
| 3 | Linear OOA(822, 1048579, F8, 2, 4) (dual of [(1048579, 2), 2097136, 5]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(822, 1048579, F8, 3, 4) (dual of [(1048579, 3), 3145715, 5]-NRT-code) | [i] | OA Folding and Stacking | |