Information on Result #701092
Linear OA(450, 69, F4, 28) (dual of [69, 19, 29]-code), using construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,47}), C2 = C([0,26]), C3 = C1 + C2 = C([0,23]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,47}) based on
- linear OA(447, 63, F4, 27) (dual of [63, 16, 28]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,47}, and minimum distance d ≥ |{−1,0,…,25}|+1 = 28 (BCH-bound) [i]
- linear OA(447, 63, F4, 27) (dual of [63, 16, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(450, 63, F4, 28) (dual of [63, 13, 29]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,47}, and minimum distance d ≥ |{−1,0,…,26}|+1 = 29 (BCH-bound) [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(40, 3, F4, 0) (dual of [3, 3, 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, 3, F4, 0) (dual of [3, 3, 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.
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 OOA(450, 34, F4, 2, 28) (dual of [(34, 2), 18, 29]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(450, 23, F4, 3, 28) (dual of [(23, 3), 19, 29]-NRT-code) | [i] | ||