Information on Result #2274374
Linear OA(4241, 1078, F4, 60) (dual of [1078, 837, 61]-code), using 1 times code embedding in larger space based on linear OA(4240, 1077, F4, 60) (dual of [1077, 837, 61]-code), using
- construction XX applied to C1 = C([1018,49]), C2 = C([0,54]), C3 = C1 + C2 = C([0,49]), and C∩ = C1 ∩ C2 = C([1018,54]) [i] based on
- linear OA(4206, 1023, F4, 55) (dual of [1023, 817, 56]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−5,−4,…,49}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(4206, 1023, F4, 55) (dual of [1023, 817, 56]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,54], and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(4226, 1023, F4, 60) (dual of [1023, 797, 61]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−5,−4,…,54}, and designed minimum distance d ≥ |I|+1 = 61 [i]
- linear OA(4186, 1023, F4, 50) (dual of [1023, 837, 51]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,49], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(47, 27, F4, 4) (dual of [27, 20, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- linear OA(47, 27, F4, 4) (dual of [27, 20, 5]-code) (see above)
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(4241, 539, F4, 2, 60) (dual of [(539, 2), 837, 61]-NRT-code) | [i] | OOA Folding | |