Information on Result #701010
Linear OA(446, 82, F4, 21) (dual of [82, 36, 22]-code), using construction XX applied to C1 = C([1,15]), C2 = C([0,11]), C3 = C1 + C2 = C([1,11]), and C∩ = C1 ∩ C2 = C([0,15]) based on
- linear OA(436, 63, F4, 20) (dual of [63, 27, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(428, 63, F4, 13) (dual of [63, 35, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(437, 63, F4, 21) (dual of [63, 26, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(427, 63, F4, 12) (dual of [63, 36, 13]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(49, 18, F4, 7) (dual of [18, 9, 8]-code), using
- construction X applied to C({0,1,3}) ⊂ C({1,3}) [i] based on
- linear OA(49, 17, F4, 7) (dual of [17, 8, 8]-code), using the cyclic code C(A) with length 17 | 44−1, defining set A = {0,1,3}, and minimum distance d ≥ |{1,5}| + |{−6,−5,…,0}∖{−3}| = 8 (general Roos-bound) [i]
- linear OA(48, 17, F4, 6) (dual of [17, 9, 7]-code), using the cyclic code C(A) with length 17 | 44−1, defining set A = {1,3}, and minimum distance d ≥ |{−5,−3,−1,…,5}|+1 = 7 (BCH-bound) [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 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
- construction X applied to C({0,1,3}) ⊂ C({1,3}) [i] based on
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(446, 82, F4, 20) (dual of [82, 36, 21]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(448, 84, F4, 21) (dual of [84, 36, 22]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(444, 80, F4, 19) (dual of [80, 36, 20]-code) | [i] | Truncation | |
| 4 | Linear OA(443, 79, F4, 18) (dual of [79, 36, 19]-code) | [i] | ||
| 5 | Linear OA(447, 84, F4, 21) (dual of [84, 37, 22]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(446, 41, F4, 2, 21) (dual of [(41, 2), 36, 22]-NRT-code) | [i] | OOA Folding | |