Information on Result #678122
Linear OA(4122, 1048587, F4, 17) (dual of [1048587, 1048465, 18]-code), using construction X applied to Ce(16) ⊂ Ce(14) based on
- linear OA(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(4111, 1048576, F4, 15) (dual of [1048576, 1048465, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(41, 11, F4, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(4123, 1048588, F4, 17) (dual of [1048588, 1048465, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4121, 1048586, F4, 16) (dual of [1048586, 1048465, 17]-code) | [i] | Truncation | |
| 3 | Linear OOA(4122, 524293, F4, 2, 17) (dual of [(524293, 2), 1048464, 18]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(4122, 349529, F4, 3, 17) (dual of [(349529, 3), 1048465, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(4122, 131073, F4, 17, 17) (dual of [(131073, 17), 2228119, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |