Information on Result #1448429
Linear OOA(8166, 2097206, F8, 2, 26) (dual of [(2097206, 2), 4194246, 27]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8166, 2097206, F8, 26) (dual of [2097206, 2097040, 27]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8165, 2097204, F8, 26) (dual of [2097204, 2097039, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [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(8113, 2097152, F8, 19) (dual of [2097152, 2097039, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(810, 52, F8, 6) (dual of [52, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- a “GraX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- linear OA(8165, 2097205, F8, 25) (dual of [2097205, 2097040, 26]-code), using Gilbert–Varšamov bound and bm = 8165 > Vbs−1(k−1) = 16179 574724 533434 078041 018139 425764 703531 655173 902861 725031 075373 437241 709077 291650 132424 643194 085261 385776 415931 973821 053253 609307 642060 234687 007276 [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
- linear OA(8165, 2097204, F8, 26) (dual of [2097204, 2097039, 27]-code), 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(8166, 1048603, F8, 3, 26) (dual of [(1048603, 3), 3145643, 27]-NRT-code) | [i] | OOA Folding | |