Information on Result #677977
Linear OA(4138, 4194342, F4, 17) (dual of [4194342, 4194204, 18]-code), using construction X applied to Ce(16) ⊂ Ce(12) based on
- linear OA(4133, 4194304, F4, 17) (dual of [4194304, 4194171, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(4100, 4194304, F4, 13) (dual of [4194304, 4194204, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(45, 38, F4, 3) (dual of [38, 33, 4]-code or 38-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(4138, 4194342, F4, 16) (dual of [4194342, 4194204, 17]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4139, 4194343, F4, 17) (dual of [4194343, 4194204, 18]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4140, 4194344, F4, 17) (dual of [4194344, 4194204, 18]-code) | [i] | ||
| 4 | Linear OA(4141, 4194345, F4, 17) (dual of [4194345, 4194204, 18]-code) | [i] | ||
| 5 | Linear OA(4142, 4194346, F4, 17) (dual of [4194346, 4194204, 18]-code) | [i] | ||
| 6 | Linear OA(4137, 4194341, F4, 16) (dual of [4194341, 4194204, 17]-code) | [i] | Truncation | |
| 7 | Linear OA(4141, 4194346, F4, 17) (dual of [4194346, 4194205, 18]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(4142, 4194348, F4, 17) (dual of [4194348, 4194206, 18]-code) | [i] | ||
| 9 | Linear OOA(4138, 2097171, F4, 2, 17) (dual of [(2097171, 2), 4194204, 18]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(4138, 1398114, F4, 3, 17) (dual of [(1398114, 3), 4194204, 18]-NRT-code) | [i] | ||
| 11 | Linear OOA(4138, 524292, F4, 17, 17) (dual of [(524292, 17), 8912826, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |