Information on Result #677905
Linear OA(4134, 4194316, F4, 17) (dual of [4194316, 4194182, 18]-code), using construction X applied to Ce(16) ⊂ Ce(14) 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(4122, 4194304, F4, 15) (dual of [4194304, 4194182, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(41, 12, F4, 1) (dual of [12, 11, 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(4135, 4194317, F4, 17) (dual of [4194317, 4194182, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4133, 4194315, F4, 16) (dual of [4194315, 4194182, 17]-code) | [i] | Truncation | |
| 3 | Linear OOA(4134, 2097158, F4, 2, 17) (dual of [(2097158, 2), 4194182, 18]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(4134, 1398105, F4, 3, 17) (dual of [(1398105, 3), 4194181, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(4134, 524289, F4, 17, 17) (dual of [(524289, 17), 8912779, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |