Information on Result #707572
Linear OA(448, 1041, F4, 12) (dual of [1041, 993, 13]-code), using construction XX applied to C1 = C([1022,8]), C2 = C([1,10]), C3 = C1 + C2 = C([1,8]), and C∩ = C1 ∩ C2 = C([1022,10]) based on
- linear OA(436, 1023, F4, 10) (dual of [1023, 987, 11]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(440, 1023, F4, 10) (dual of [1023, 983, 11]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(446, 1023, F4, 12) (dual of [1023, 977, 13]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(430, 1023, F4, 8) (dual of [1023, 993, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 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
- 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 (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(449, 1043, F4, 12) (dual of [1043, 994, 13]-code) | [i] | Construction X with Varšamov Bound | |
| 2 | Linear OOA(448, 520, F4, 2, 12) (dual of [(520, 2), 992, 13]-NRT-code) | [i] | OOA Folding | |