Information on Result #677903
Linear OA(4144, 4194315, F4, 18) (dual of [4194315, 4194171, 19]-code), using construction X applied to Ce(17) ⊂ Ce(16) based on
- linear OA(4144, 4194304, F4, 18) (dual of [4194304, 4194160, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- 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(40, 11, F4, 0) (dual of [11, 11, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-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(4145, 4194316, F4, 18) (dual of [4194316, 4194171, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4146, 4194317, F4, 18) (dual of [4194317, 4194171, 19]-code) | [i] | ||
| 3 | Linear OOA(4144, 2097157, F4, 2, 18) (dual of [(2097157, 2), 4194170, 19]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(4144, 1398105, F4, 3, 18) (dual of [(1398105, 3), 4194171, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(4144, 466035, F4, 18, 18) (dual of [(466035, 18), 8388486, 19]-NRT-code) | [i] | OA Folding and Stacking | |