Information on Result #737400
Linear OA(4217, 1095, F4, 51) (dual of [1095, 878, 52]-code), using construction X applied to Ce(50) ⊂ Ce(38) based on
- linear OA(4191, 1024, F4, 51) (dual of [1024, 833, 52]-code), using an extension Ce(50) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(4146, 1024, F4, 39) (dual of [1024, 878, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(426, 71, F4, 11) (dual of [71, 45, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(426, 72, F4, 11) (dual of [72, 46, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
- linear OA(425, 65, F4, 11) (dual of [65, 40, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(419, 65, F4, 9) (dual of [65, 46, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
- discarding factors / shortening the dual code based on linear OA(426, 72, F4, 11) (dual of [72, 46, 12]-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(4218, 1096, F4, 51) (dual of [1096, 878, 52]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4220, 1098, F4, 51) (dual of [1098, 878, 52]-code) | [i] | ||