Information on Result #1443563
Linear OOA(858, 262161, F8, 2, 11) (dual of [(262161, 2), 524264, 12]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(858, 262161, F8, 11) (dual of [262161, 262103, 12]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(856, 262158, F8, 11) (dual of [262158, 262102, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- 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(843, 262144, F8, 9) (dual of [262144, 262101, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(10) ⊂ Ce(8) [i] based on
- linear OA(856, 262159, F8, 9) (dual of [262159, 262103, 10]-code), using Gilbert–Varšamov bound and bm = 856 > Vbs−1(k−1) = 3189 511891 402191 653256 900365 834789 805221 378311 [i]
- linear OA(81, 2, F8, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(856, 262158, F8, 11) (dual of [262158, 262102, 12]-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(858, 131080, F8, 3, 11) (dual of [(131080, 3), 393182, 12]-NRT-code) | [i] | OOA Folding | |