Information on Result #1558258
Linear OOA(8157, 1048581, F8, 3, 26) (dual of [(1048581, 3), 3145586, 27]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(8157, 1048581, F8, 2, 26) (dual of [(1048581, 2), 2097005, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8157, 2097162, F8, 26) (dual of [2097162, 2097005, 27]-code), using
- construction XX applied to Ce(25) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- linear OA(8155, 2097152, F8, 26) (dual of [2097152, 2096997, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8141, 2097152, F8, 23) (dual of [2097152, 2097011, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(80, 8, F8, 0) (dual of [8, 8, 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
- linear OA(81, 2, F8, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(25) ⊂ Ce(24) ⊂ Ce(22) [i] based on
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(8157, 209716, F8, 33, 26) (dual of [(209716, 33), 6920471, 27]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |