Information on Result #708862
Linear OA(4198, 1084, F4, 48) (dual of [1084, 886, 49]-code), using construction XX applied to C1 = C([1017,36]), C2 = C([0,41]), C3 = C1 + C2 = C([0,36]), and C∩ = C1 ∩ C2 = C([1017,41]) based on
- linear OA(4161, 1023, F4, 43) (dual of [1023, 862, 44]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−6,−5,…,36}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(4156, 1023, F4, 42) (dual of [1023, 867, 43]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,41], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(4181, 1023, F4, 48) (dual of [1023, 842, 49]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−6,−5,…,41}, and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(4136, 1023, F4, 37) (dual of [1023, 887, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(410, 34, F4, 5) (dual of [34, 24, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- 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
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(4199, 1085, F4, 48) (dual of [1085, 886, 49]-code) | [i] | Code Embedding in Larger Space | |
2 | Linear OA(4200, 1086, F4, 48) (dual of [1086, 886, 49]-code) | [i] | ||
3 | Linear OOA(4198, 542, F4, 2, 48) (dual of [(542, 2), 886, 49]-NRT-code) | [i] | OOA Folding |