Information on Result #701602
Linear OA(921, 44, F9, 13) (dual of [44, 23, 14]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,6,7,8,10,31}), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,5,6,7,8,10,11,31}) based on
- linear OA(919, 40, F9, 12) (dual of [40, 21, 13]-code), using the cyclic code C(A) with length 40 | 92−1, defining set A = {0,1,2,3,4,5,6,7,8,10,31}, and minimum distance d ≥ |{−1,0,…,10}|+1 = 13 (BCH-bound) [i]
- linear OA(919, 40, F9, 12) (dual of [40, 21, 13]-code), using the expurgated narrow-sense BCH-code C(I) with length 40 | 92−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(921, 40, F9, 13) (dual of [40, 19, 14]-code), using the cyclic code C(A) with length 40 | 92−1, defining set A = {0,1,2,3,4,5,6,7,8,10,11,31}, and minimum distance d ≥ |{−1,0,…,11}|+1 = 14 (BCH-bound) [i]
- linear OA(917, 40, F9, 11) (dual of [40, 23, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 40 | 92−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(90, 2, F9, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(90, 2, F9, 0) (dual of [2, 2, 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(921, 22, F9, 2, 13) (dual of [(22, 2), 23, 14]-NRT-code) | [i] | OOA Folding | |