Information on Result #1307671
Linear OA(458, 293, F4, 18) (dual of [293, 235, 19]-code), using 28 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 11 times 0) based on linear OA(451, 258, F4, 18) (dual of [258, 207, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(451, 256, F4, 18) (dual of [256, 205, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- 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(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
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(458, 293, F4, 2, 18) (dual of [(293, 2), 528, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(458, 293, F4, 3, 18) (dual of [(293, 3), 821, 19]-NRT-code) | [i] | ||
| 3 | Digital (40, 58, 293)-net over F4 | [i] | ||