Information on Result #1300726
Linear OA(4199, 256, F4, 100) (dual of [256, 57, 101]-code), using construction X with Varšamov bound based on
- linear OA(4198, 254, F4, 100) (dual of [254, 56, 101]-code), using
- 2 times truncation [i] based on linear OA(4200, 256, F4, 102) (dual of [256, 56, 103]-code), using
- an extension Ce(101) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,101], and designed minimum distance d ≥ |I|+1 = 102 [i]
- 2 times truncation [i] based on linear OA(4200, 256, F4, 102) (dual of [256, 56, 103]-code), using
- linear OA(4198, 255, F4, 99) (dual of [255, 57, 100]-code), using Gilbert–Varšamov bound and bm = 4198 > Vbs−1(k−1) = 134763 554912 640364 898188 939307 355776 312009 508056 727002 102214 114587 621349 926429 768987 120693 311168 480021 020735 460899 452206 [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, using
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(4200, 258, F4, 100) (dual of [258, 58, 101]-code) | [i] | Construction X with Varšamov Bound | |