Information on Result #709563
Linear OA(4250, 1077, F4, 63) (dual of [1077, 827, 64]-code), using construction XX applied to C1 = C([1018,52]), C2 = C([0,57]), C3 = C1 + C2 = C([0,52]), and C∩ = C1 ∩ C2 = C([1018,57]) 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(4216, 1023, F4, 58) (dual of [1023, 807, 59]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,57], and designed minimum distance d ≥ |I|+1 = 59 [i]
- linear OA(4236, 1023, F4, 63) (dual of [1023, 787, 64]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−5,−4,…,57}, and designed minimum distance d ≥ |I|+1 = 64 [i]
- linear OA(4196, 1023, F4, 53) (dual of [1023, 827, 54]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,52], and designed minimum distance d ≥ |I|+1 = 54 [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 OA(4251, 1078, F4, 63) (dual of [1078, 827, 64]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4252, 1079, F4, 63) (dual of [1079, 827, 64]-code) | [i] | ||
| 3 | Linear OOA(4250, 538, F4, 2, 63) (dual of [(538, 2), 826, 64]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(4250, 359, F4, 3, 63) (dual of [(359, 3), 827, 64]-NRT-code) | [i] | ||