Information on Result #709030
Linear OA(4202, 1064, F4, 51) (dual of [1064, 862, 52]-code), using construction XX applied to C1 = C([293,341]), C2 = C([299,343]), C3 = C1 + C2 = C([299,341]), and C∩ = C1 ∩ C2 = C([293,343]) based on
- linear OA(4181, 1023, F4, 49) (dual of [1023, 842, 50]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {293,294,…,341}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(4171, 1023, F4, 45) (dual of [1023, 852, 46]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {299,300,…,343}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(4191, 1023, F4, 51) (dual of [1023, 832, 52]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {293,294,…,343}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- 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 = {299,300,…,341}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(410, 30, F4, 5) (dual of [30, 20, 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(41, 11, F4, 1) (dual of [11, 10, 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
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(4202, 532, F4, 2, 51) (dual of [(532, 2), 862, 52]-NRT-code) | [i] | OOA Folding | |