Information on Result #1307734
Linear OA(463, 282, F4, 20) (dual of [282, 219, 21]-code), using 15 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 4 times 0, 1, 7 times 0) based on linear OA(459, 263, F4, 20) (dual of [263, 204, 21]-code), using
- construction XX applied to C1 = C([254,17]), C2 = C([0,18]), C3 = C1 + C2 = C([0,17]), and C∩ = C1 ∩ C2 = C([254,18]) [i] based on
- linear OA(455, 255, F4, 19) (dual of [255, 200, 20]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−1,0,…,17}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(455, 255, F4, 19) (dual of [255, 200, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(459, 255, F4, 20) (dual of [255, 196, 21]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−1,0,…,18}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(451, 255, F4, 18) (dual of [255, 204, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(40, 4, F4, 0) (dual of [4, 4, 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(40, 4, F4, 0) (dual of [4, 4, 1]-code) (see above)
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(463, 282, F4, 2, 20) (dual of [(282, 2), 501, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(463, 282, F4, 3, 20) (dual of [(282, 3), 783, 21]-NRT-code) | [i] | ||
| 3 | Digital (43, 63, 282)-net over F4 | [i] | ||