Information on Result #709697
Linear OA(4257, 1039, F4, 72) (dual of [1039, 782, 73]-code), using construction XX applied to C1 = C([1021,68]), C2 = C([0,69]), C3 = C1 + C2 = C([0,68]), and C∩ = C1 ∩ C2 = C([1021,69]) based on
- linear OA(4251, 1023, F4, 71) (dual of [1023, 772, 72]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−2,−1,…,68}, and designed minimum distance d ≥ |I|+1 = 72 [i]
- linear OA(4246, 1023, F4, 70) (dual of [1023, 777, 71]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,69], and designed minimum distance d ≥ |I|+1 = 71 [i]
- linear OA(4256, 1023, F4, 72) (dual of [1023, 767, 73]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−2,−1,…,69}, and designed minimum distance d ≥ |I|+1 = 73 [i]
- linear OA(4241, 1023, F4, 69) (dual of [1023, 782, 70]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,68], and designed minimum distance d ≥ |I|+1 = 70 [i]
- 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, 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(4257, 519, F4, 2, 72) (dual of [(519, 2), 781, 73]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4257, 346, F4, 3, 72) (dual of [(346, 3), 781, 73]-NRT-code) | [i] | ||