Information on Result #707689
Linear OA(471, 1048, F4, 18) (dual of [1048, 977, 19]-code), using construction XX applied to C1 = C([1019,12]), C2 = C([0,13]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([1019,13]) based on
- linear OA(461, 1023, F4, 17) (dual of [1023, 962, 18]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,12}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(451, 1023, F4, 14) (dual of [1023, 972, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(466, 1023, F4, 18) (dual of [1023, 957, 19]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,13}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(446, 1023, F4, 13) (dual of [1023, 977, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(45, 20, F4, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-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(471, 524, F4, 2, 18) (dual of [(524, 2), 977, 19]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(471, 349, F4, 3, 18) (dual of [(349, 3), 976, 19]-NRT-code) | [i] | ||