Information on Result #1301079
Linear OA(4242, 4104, F4, 54) (dual of [4104, 3862, 55]-code), using construction X with Varšamov bound based on
- linear OA(4241, 4102, F4, 54) (dual of [4102, 3861, 55]-code), using
- construction X applied to Ce(53) ⊂ Ce(52) [i] based on
- linear OA(4241, 4096, F4, 54) (dual of [4096, 3855, 55]-code), using an extension Ce(53) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,53], and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(4235, 4096, F4, 53) (dual of [4096, 3861, 54]-code), using an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(40, 6, F4, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(53) ⊂ Ce(52) [i] based on
- linear OA(4241, 4103, F4, 53) (dual of [4103, 3862, 54]-code), using Gilbert–Varšamov bound and bm = 4241 > Vbs−1(k−1) = 4 368306 506734 421542 702600 388592 582285 847663 845171 109161 757220 291726 269913 271668 096782 793806 368082 365832 566310 960536 663576 809208 999215 652118 004992 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
Mode: 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(4242, 2052, F4, 2, 54) (dual of [(2052, 2), 3862, 55]-NRT-code) | [i] | OOA Folding | |