Information on Result #707680
Linear OA(456, 1033, F4, 15) (dual of [1033, 977, 16]-code), using construction XX applied to C1 = C([1022,12]), C2 = C([0,13]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([1022,13]) based on
- linear OA(451, 1023, F4, 14) (dual of [1023, 972, 15]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,12}, and designed minimum distance d ≥ |I|+1 = 15 [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(456, 1023, F4, 15) (dual of [1023, 967, 16]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,13}, and designed minimum distance d ≥ |I|+1 = 16 [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(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
- linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-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(461, 1060, F4, 15) (dual of [1060, 999, 16]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(462, 1084, F4, 15) (dual of [1084, 1022, 16]-code) | [i] | ||
| 3 | Linear OA(463, 1126, F4, 15) (dual of [1126, 1063, 16]-code) | [i] | ||
| 4 | Linear OA(464, 1192, F4, 15) (dual of [1192, 1128, 16]-code) | [i] | ||
| 5 | Linear OA(465, 1286, F4, 15) (dual of [1286, 1221, 16]-code) | [i] | ||
| 6 | Linear OA(466, 1404, F4, 15) (dual of [1404, 1338, 16]-code) | [i] | ||
| 7 | Linear OOA(456, 516, F4, 2, 15) (dual of [(516, 2), 976, 16]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(456, 344, F4, 3, 15) (dual of [(344, 3), 976, 16]-NRT-code) | [i] | ||