Information on Result #2242270
Linear OA(4113, 262175, F4, 16) (dual of [262175, 262062, 17]-code), using 1 times truncation based on linear OA(4114, 262176, F4, 17) (dual of [262176, 262062, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(4109, 262144, F4, 17) (dual of [262144, 262035, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(482, 262144, F4, 13) (dual of [262144, 262062, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-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
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(4115, 262177, F4, 16) (dual of [262177, 262062, 17]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4113, 132063, F4, 2, 16) (dual of [(132063, 2), 264013, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4113, 132063, F4, 3, 16) (dual of [(132063, 3), 396076, 17]-NRT-code) | [i] | ||
| 4 | Digital (97, 113, 132063)-net over F4 | [i] | ||
| 5 | Linear OA(4115, 262178, F4, 16) (dual of [262178, 262063, 17]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(4113, 131087, F4, 2, 16) (dual of [(131087, 2), 262061, 17]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4113, 87391, F4, 3, 16) (dual of [(87391, 3), 262060, 17]-NRT-code) | [i] | ||
| 8 | Linear OOA(4113, 32771, F4, 16, 16) (dual of [(32771, 16), 524223, 17]-NRT-code) | [i] | OA Folding and Stacking | |