Information on Result #708153
Linear OA(4101, 1033, F4, 27) (dual of [1033, 932, 28]-code), using construction XX applied to C1 = C([1022,24]), C2 = C([0,25]), C3 = C1 + C2 = C([0,24]), and C∩ = C1 ∩ C2 = C([1022,25]) based on
- linear OA(496, 1023, F4, 26) (dual of [1023, 927, 27]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,24}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(496, 1023, F4, 26) (dual of [1023, 927, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(4101, 1023, F4, 27) (dual of [1023, 922, 28]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,25}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(491, 1023, F4, 25) (dual of [1023, 932, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [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(4104, 1042, F4, 27) (dual of [1042, 938, 28]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(4105, 1052, F4, 27) (dual of [1052, 947, 28]-code) | [i] | ||
| 3 | Linear OA(4106, 1070, F4, 27) (dual of [1070, 964, 28]-code) | [i] | ||
| 4 | Linear OA(4107, 1099, F4, 27) (dual of [1099, 992, 28]-code) | [i] | ||
| 5 | Linear OA(4108, 1141, F4, 27) (dual of [1141, 1033, 28]-code) | [i] | ||
| 6 | Linear OA(4109, 1194, F4, 27) (dual of [1194, 1085, 28]-code) | [i] | ||
| 7 | Linear OA(4110, 1255, F4, 27) (dual of [1255, 1145, 28]-code) | [i] | ||
| 8 | Linear OOA(4101, 516, F4, 2, 27) (dual of [(516, 2), 931, 28]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(4101, 344, F4, 3, 27) (dual of [(344, 3), 931, 28]-NRT-code) | [i] | ||