Information on Result #1300665
Linear OA(4191, 274, F4, 89) (dual of [274, 83, 90]-code), using construction X with Varšamov bound based on
- linear OA(4190, 272, F4, 89) (dual of [272, 82, 90]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4188, 269, F4, 89) (dual of [269, 81, 90]-code), using
- construction X applied to Ce(89) ⊂ Ce(84) [i] based on
- linear OA(4184, 256, F4, 90) (dual of [256, 72, 91]-code), using an extension Ce(89) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,89], and designed minimum distance d ≥ |I|+1 = 90 [i]
- linear OA(4175, 256, F4, 85) (dual of [256, 81, 86]-code), using an extension Ce(84) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,84], and designed minimum distance d ≥ |I|+1 = 85 [i]
- linear OA(44, 13, F4, 3) (dual of [13, 9, 4]-code or 13-cap in PG(3,4)), using
- construction X applied to Ce(89) ⊂ Ce(84) [i] based on
- linear OA(4188, 270, F4, 87) (dual of [270, 82, 88]-code), using Gilbert–Varšamov bound and bm = 4188 > Vbs−1(k−1) = 107277 071665 019478 861981 559207 621602 644072 679882 417241 236684 317833 775194 959814 465816 043375 166127 375259 212096 037824 [i]
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(4188, 269, F4, 89) (dual of [269, 81, 90]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4190, 273, F4, 88) (dual of [273, 83, 89]-code), using Gilbert–Varšamov bound and bm = 4190 > Vbs−1(k−1) = 2 163135 750087 732606 688243 704428 425778 420809 305394 568671 401710 472357 736155 696430 740157 905680 461270 812115 559042 168656 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 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 OA(4192, 276, F4, 89) (dual of [276, 84, 90]-code) | [i] | Construction X with Varšamov Bound | |