Information on Result #709411
Linear OA(4237, 1065, F4, 60) (dual of [1065, 828, 61]-code), using construction XX applied to C1 = C([1018,52]), C2 = C([1,54]), C3 = C1 + C2 = C([1,52]), and C∩ = C1 ∩ C2 = C([1018,54]) based on
- linear OA(4216, 1023, F4, 58) (dual of [1023, 807, 59]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−5,−4,…,52}, and designed minimum distance d ≥ |I|+1 = 59 [i]
- linear OA(4205, 1023, F4, 54) (dual of [1023, 818, 55]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,54], and designed minimum distance d ≥ |I|+1 = 55 [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(4195, 1023, F4, 52) (dual of [1023, 828, 53]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(410, 31, F4, 5) (dual of [31, 21, 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(4237, 355, F4, 3, 60) (dual of [(355, 3), 828, 61]-NRT-code) | [i] | OOA Folding | |