Information on Result #681850
Linear OA(451, 263, F4, 17) (dual of [263, 212, 18]-code), using construction XX applied to Ce(16) ⊂ Ce(14) ⊂ Ce(13) based on
- linear OA(449, 256, F4, 17) (dual of [256, 207, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(445, 256, F4, 15) (dual of [256, 211, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(441, 256, F4, 14) (dual of [256, 215, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(41, 6, F4, 1) (dual of [6, 5, 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(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
Mode: Constructive and 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(451, 208, F4, 2, 17) (dual of [(208, 2), 365, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(451, 208, F4, 3, 17) (dual of [(208, 3), 573, 18]-NRT-code) | [i] | ||
| 3 | Digital (34, 51, 208)-net over F4 | [i] | ||