Information on Result #823723
Linear OOA(4157, 524306, F4, 2, 21) (dual of [(524306, 2), 1048455, 22]-NRT-code), using OOA 2-folding based on linear OA(4157, 1048612, F4, 21) (dual of [1048612, 1048455, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4156, 1048611, F4, 21) (dual of [1048611, 1048455, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(45, 35, F4, 3) (dual of [35, 30, 4]-code or 35-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
- construction X applied to Ce(20) ⊂ Ce(16) [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 OOA(4157, 524306, F4, 2, 20) (dual of [(524306, 2), 1048455, 21]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(4159, 524307, F4, 2, 21) (dual of [(524307, 2), 1048455, 22]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(4158, 524306, F4, 2, 21) (dual of [(524306, 2), 1048454, 22]-NRT-code) | [i] | OOA Duplication | |
| 4 | Linear OOA(4157, 384945, F4, 3, 21) (dual of [(384945, 3), 1154678, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (136, 157, 384945)-net over F4 | [i] | ||