Information on Result #682834
Linear OA(584, 15649, F5, 17) (dual of [15649, 15565, 18]-code), using construction XX applied to Ce(16) ⊂ Ce(12) ⊂ Ce(11) based on
- linear OA(579, 15625, F5, 17) (dual of [15625, 15546, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(561, 15625, F5, 13) (dual of [15625, 15564, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(555, 15625, F5, 12) (dual of [15625, 15570, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(54, 23, F5, 3) (dual of [23, 19, 4]-code or 23-cap in PG(3,5)), using
- linear OA(50, 1, F5, 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(584, 11829, F5, 2, 17) (dual of [(11829, 2), 23574, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(584, 11829, F5, 3, 17) (dual of [(11829, 3), 35403, 18]-NRT-code) | [i] | ||
| 3 | Digital (67, 84, 11829)-net over F5 | [i] | ||
| 4 | Linear OOA(584, 7824, F5, 2, 17) (dual of [(7824, 2), 15564, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(584, 5216, F5, 3, 17) (dual of [(5216, 3), 15564, 18]-NRT-code) | [i] | ||
| 6 | Linear OOA(584, 1956, F5, 17, 17) (dual of [(1956, 17), 33168, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |