Information on Result #1323906
Linear OA(4128, 16442, F4, 22) (dual of [16442, 16314, 23]-code), using construction X with Varšamov bound based on
- linear OA(4127, 16440, F4, 22) (dual of [16440, 16313, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
- linear OA(4113, 16384, F4, 22) (dual of [16384, 16271, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(471, 16384, F4, 14) (dual of [16384, 16313, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(21) ⊂ Ce(13) [i] based on
- linear OA(4127, 16441, F4, 21) (dual of [16441, 16314, 22]-code), using Gilbert–Varšamov bound and bm = 4127 > Vbs−1(k−1) = 2947 758405 222521 245059 642476 269911 935121 817372 731928 928284 033277 609057 792989 [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 OOA(4128, 16442, F4, 2, 22) (dual of [(16442, 2), 32756, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4128, 16442, F4, 3, 22) (dual of [(16442, 3), 49198, 23]-NRT-code) | [i] | ||
| 3 | Digital (106, 128, 16442)-net over F4 | [i] | ||
| 4 | Linear OOA(4128, 8221, F4, 2, 22) (dual of [(8221, 2), 16314, 23]-NRT-code) | [i] | OOA Folding | |