Information on Result #678687
Linear OA(4246, 65565, F4, 41) (dual of [65565, 65319, 42]-code), using construction X applied to Ce(40) ⊂ Ce(36) based on
- linear OA(4241, 65536, F4, 41) (dual of [65536, 65295, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(45, 29, F4, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(4246, 65565, F4, 40) (dual of [65565, 65319, 41]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4247, 65566, F4, 41) (dual of [65566, 65319, 42]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4245, 65564, F4, 40) (dual of [65564, 65319, 41]-code) | [i] | Truncation | |
| 4 | Linear OOA(4246, 32782, F4, 2, 41) (dual of [(32782, 2), 65318, 42]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4246, 21855, F4, 3, 41) (dual of [(21855, 3), 65319, 42]-NRT-code) | [i] | ||
| 6 | Linear OOA(4246, 3278, F4, 41, 41) (dual of [(3278, 41), 134152, 42]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |