Information on Result #737199
Linear OA(4207, 262215, F4, 29) (dual of [262215, 262008, 30]-code), using construction X applied to Ce(28) ⊂ Ce(20) based on
- linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(417, 71, F4, 7) (dual of [71, 54, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 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
- construction X applied to Ce(6) ⊂ Ce(4) [i] based on
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(4207, 262215, F4, 28) (dual of [262215, 262008, 29]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4209, 262217, F4, 29) (dual of [262217, 262008, 30]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4210, 262218, F4, 29) (dual of [262218, 262008, 30]-code) | [i] | ||
| 4 | Linear OOA(4207, 131107, F4, 2, 29) (dual of [(131107, 2), 262007, 30]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4207, 87405, F4, 3, 29) (dual of [(87405, 3), 262008, 30]-NRT-code) | [i] | ||