Information on Result #679367
Linear OA(492, 16413, F4, 17) (dual of [16413, 16321, 18]-code), using construction XX applied to Ce(16) ⊂ Ce(12) ⊂ Ce(10) based on
- linear OA(485, 16384, F4, 17) (dual of [16384, 16299, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(464, 16384, F4, 13) (dual of [16384, 16320, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(457, 16384, F4, 11) (dual of [16384, 16327, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(45, 27, F4, 3) (dual of [27, 22, 4]-code or 27-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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 OA(491, 16412, F4, 16) (dual of [16412, 16321, 17]-code) | [i] | Truncation | |
| 2 | Linear OOA(492, 9608, F4, 2, 17) (dual of [(9608, 2), 19124, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(492, 9608, F4, 3, 17) (dual of [(9608, 3), 28732, 18]-NRT-code) | [i] | ||
| 4 | Digital (75, 92, 9608)-net over F4 | [i] | ||
| 5 | Linear OOA(492, 5471, F4, 3, 17) (dual of [(5471, 3), 16321, 18]-NRT-code) | [i] | OOA Folding | |