Information on Result #707711
Linear OA(461, 1033, F4, 16) (dual of [1033, 972, 17]-code), using construction XX applied to C1 = C([1022,13]), C2 = C([0,14]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([1022,14]) based on
- 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(456, 1023, F4, 15) (dual of [1023, 967, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(461, 1023, F4, 16) (dual of [1023, 962, 17]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,14}, and designed minimum distance d ≥ |I|+1 = 17 [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(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(464, 1044, F4, 16) (dual of [1044, 980, 17]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(465, 1058, F4, 16) (dual of [1058, 993, 17]-code) | [i] | ||
| 3 | Linear OA(466, 1083, F4, 16) (dual of [1083, 1017, 17]-code) | [i] | ||
| 4 | Linear OA(467, 1126, F4, 16) (dual of [1126, 1059, 17]-code) | [i] | ||
| 5 | Linear OA(468, 1192, F4, 16) (dual of [1192, 1124, 17]-code) | [i] | ||
| 6 | Linear OA(469, 1283, F4, 16) (dual of [1283, 1214, 17]-code) | [i] | ||
| 7 | Linear OOA(461, 516, F4, 2, 16) (dual of [(516, 2), 971, 17]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(461, 344, F4, 3, 16) (dual of [(344, 3), 971, 17]-NRT-code) | [i] | ||