Information on Result #681186
Linear OA(468, 1032, F4, 18) (dual of [1032, 964, 19]-code), using construction XX applied to Ce(17) ⊂ Ce(16) ⊂ Ce(14) based on
- linear OA(466, 1024, F4, 18) (dual of [1024, 958, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(461, 1024, F4, 17) (dual of [1024, 963, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(456, 1024, F4, 15) (dual of [1024, 968, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(40, 6, F4, 0) (dual of [6, 6, 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(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(468, 741, F4, 2, 18) (dual of [(741, 2), 1414, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(468, 741, F4, 3, 18) (dual of [(741, 3), 2155, 19]-NRT-code) | [i] | ||
| 3 | Digital (50, 68, 741)-net over F4 | [i] | ||