Information on Result #678713
Linear OA(4102, 65565, F4, 17) (dual of [65565, 65463, 18]-code), using construction X applied to Ce(16) ⊂ Ce(12) based on
- linear OA(497, 65536, F4, 17) (dual of [65536, 65439, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(4102, 65565, F4, 16) (dual of [65565, 65463, 17]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4103, 65566, F4, 17) (dual of [65566, 65463, 18]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4101, 65564, F4, 16) (dual of [65564, 65463, 17]-code) | [i] | Truncation | |
| 4 | Linear OOA(4102, 32782, F4, 2, 17) (dual of [(32782, 2), 65462, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4102, 21855, F4, 3, 17) (dual of [(21855, 3), 65463, 18]-NRT-code) | [i] | ||
| 6 | Linear OOA(4102, 8195, F4, 17, 17) (dual of [(8195, 17), 139213, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |