Information on Result #678739
Linear OA(4128, 65575, F4, 20) (dual of [65575, 65447, 21]-code), using construction X applied to Ce(20) ⊂ Ce(14) based on
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(489, 65536, F4, 15) (dual of [65536, 65447, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), 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(4129, 65576, F4, 20) (dual of [65576, 65447, 21]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4128, 44539, F4, 2, 20) (dual of [(44539, 2), 88950, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4128, 44539, F4, 3, 20) (dual of [(44539, 3), 133489, 21]-NRT-code) | [i] | ||
| 4 | Digital (108, 128, 44539)-net over F4 | [i] | ||
| 5 | Linear OA(4130, 65578, F4, 20) (dual of [65578, 65448, 21]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(4128, 32787, F4, 2, 20) (dual of [(32787, 2), 65446, 21]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4128, 21858, F4, 3, 20) (dual of [(21858, 3), 65446, 21]-NRT-code) | [i] | ||
| 8 | Linear OOA(4128, 6557, F4, 20, 20) (dual of [(6557, 20), 131012, 21]-NRT-code) | [i] | OA Folding and Stacking | |