Information on Result #1435471
Linear OOA(4255, 16444, F4, 2, 46) (dual of [(16444, 2), 32633, 47]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4255, 16444, F4, 46) (dual of [16444, 16189, 47]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4253, 16440, F4, 46) (dual of [16440, 16187, 47]-code), using
- construction X applied to Ce(45) ⊂ Ce(37) [i] based on
- linear OA(4239, 16384, F4, 46) (dual of [16384, 16145, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(4197, 16384, F4, 38) (dual of [16384, 16187, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(414, 56, F4, 7) (dual of [56, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- construction X applied to Ce(45) ⊂ Ce(37) [i] based on
- linear OA(4253, 16442, F4, 45) (dual of [16442, 16189, 46]-code), using Gilbert–Varšamov bound and bm = 4253 > Vbs−1(k−1) = 110 906138 771046 818082 252453 537836 231744 527372 029579 532127 853337 713422 249989 960172 531381 965733 307572 907936 473612 143102 027276 212782 425023 227126 032641 880252 [i]
- linear OA(40, 2, F4, 0) (dual of [2, 2, 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
- linear OA(4253, 16440, F4, 46) (dual of [16440, 16187, 47]-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(4255, 8222, F4, 3, 46) (dual of [(8222, 3), 24411, 47]-NRT-code) | [i] | OOA Folding | |