Information on Result #682839
Linear OA(578, 15649, F5, 16) (dual of [15649, 15571, 17]-code), using construction XX applied to Ce(15) ⊂ Ce(11) ⊂ Ce(10) based on
- linear OA(573, 15625, F5, 16) (dual of [15625, 15552, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(549, 15625, F5, 11) (dual of [15625, 15576, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(578, 10552, F5, 2, 16) (dual of [(10552, 2), 21026, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(578, 10552, F5, 3, 16) (dual of [(10552, 3), 31578, 17]-NRT-code) | [i] | ||
| 3 | Digital (62, 78, 10552)-net over F5 | [i] | ||
| 4 | Linear OOA(578, 7824, F5, 2, 16) (dual of [(7824, 2), 15570, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(578, 5216, F5, 3, 16) (dual of [(5216, 3), 15570, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(578, 1956, F5, 16, 16) (dual of [(1956, 16), 31218, 17]-NRT-code) | [i] | OA Folding and Stacking | |