Information on Result #678232
Linear OA(4139, 1048624, F4, 18) (dual of [1048624, 1048485, 19]-code), using construction X applied to Ce(17) ⊂ Ce(12) based on
- linear OA(4131, 1048576, F4, 18) (dual of [1048576, 1048445, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(48, 48, F4, 4) (dual of [48, 40, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 5]-code), 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(4140, 1048625, F4, 18) (dual of [1048625, 1048485, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4141, 1048626, F4, 18) (dual of [1048626, 1048485, 19]-code) | [i] | ||
| 3 | Linear OA(4142, 1048627, F4, 18) (dual of [1048627, 1048485, 19]-code) | [i] | ||
| 4 | Linear OA(4143, 1048628, F4, 18) (dual of [1048628, 1048485, 19]-code) | [i] | ||
| 5 | Linear OA(4142, 1048628, F4, 18) (dual of [1048628, 1048486, 19]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(4143, 1048630, F4, 18) (dual of [1048630, 1048487, 19]-code) | [i] | ||
| 7 | Linear OOA(4139, 524312, F4, 2, 18) (dual of [(524312, 2), 1048485, 19]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(4139, 349541, F4, 3, 18) (dual of [(349541, 3), 1048484, 19]-NRT-code) | [i] | ||