Information on Result #701046
Linear OA(453, 82, F4, 24) (dual of [82, 29, 25]-code), using construction XX applied to C1 = C({1,2,3,5,7,9,10,11,13,14,15,21,22,23}), C2 = C([0,21]), C3 = C1 + C2 = C({1,2,3,5,7,9,10,11,13,14,15,21}), and C∩ = C1 ∩ C2 = C([0,23]) based on
- linear OA(440, 63, F4, 17) (dual of [63, 23, 18]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {1,2,3,5,7,9,10,11,13,14,15,21,22,23}, and minimum distance d ≥ |{7,8,…,23}|+1 = 18 (BCH-bound) [i]
- linear OA(438, 63, F4, 22) (dual of [63, 25, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(444, 63, F4, 26) (dual of [63, 19, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,23], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(434, 63, F4, 15) (dual of [63, 29, 16]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {1,2,3,5,7,9,10,11,13,14,15,21}, and minimum distance d ≥ |{7,8,…,21}|+1 = 16 (BCH-bound) [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 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(48, 12, F4, 6) (dual of [12, 4, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 16, F4, 6) (dual of [16, 8, 7]-code), using
- an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15 = 42−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(48, 16, F4, 6) (dual of [16, 8, 7]-code), 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(4132, 158, F4, 49) (dual of [158, 26, 50]-code) | [i] | Repeating Each Code Word | |
| 2 | Linear OA(4131, 156, F4, 49) (dual of [156, 25, 50]-code) | [i] | ||
| 3 | Linear OA(4130, 154, F4, 49) (dual of [154, 24, 50]-code) | [i] | ||
| 4 | Linear OA(4129, 152, F4, 49) (dual of [152, 23, 50]-code) | [i] | ||
| 5 | Linear OA(4128, 150, F4, 49) (dual of [150, 22, 50]-code) | [i] | ||
| 6 | Linear OOA(453, 41, F4, 2, 24) (dual of [(41, 2), 29, 25]-NRT-code) | [i] | OOA Folding | |