Information on Result #2273924
Linear OA(4213, 1096, F4, 50) (dual of [1096, 883, 51]-code), using 1 times code embedding in larger space based on linear OA(4212, 1095, F4, 50) (dual of [1095, 883, 51]-code), using
- construction X applied to Ce(49) ⊂ Ce(37) [i] based on
- linear OA(4186, 1024, F4, 50) (dual of [1024, 838, 51]-code), using an extension Ce(49) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(4141, 1024, F4, 38) (dual of [1024, 883, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [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 OOA(4213, 548, F4, 2, 50) (dual of [(548, 2), 883, 51]-NRT-code) | [i] | OOA Folding | |