Information on Result #737287
Linear OA(4258, 16473, F4, 44) (dual of [16473, 16215, 45]-code), using construction X applied to Ce(44) ⊂ Ce(32) based on
- linear OA(4232, 16384, F4, 45) (dual of [16384, 16152, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(4169, 16384, F4, 33) (dual of [16384, 16215, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(426, 89, F4, 10) (dual of [89, 63, 11]-code), using
- construction X applied to C({2,5,6,7,14,17,21}) ⊂ C({2,5,6,14,17,21}) [i] based on
- linear OA(426, 85, F4, 10) (dual of [85, 59, 11]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {2,5,6,7,14,17,21}, and minimum distance d ≥ |{−4,−1,2,…,23}|+1 = 11 (BCH-bound) [i]
- linear OA(422, 85, F4, 9) (dual of [85, 63, 10]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {2,5,6,14,17,21}, and minimum distance d ≥ |{−4,−1,2,…,20}|+1 = 10 (BCH-bound) [i]
- linear OA(40, 4, F4, 0) (dual of [4, 4, 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({2,5,6,7,14,17,21}) ⊂ C({2,5,6,14,17,21}) [i] based on
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 OA(4259, 16474, F4, 44) (dual of [16474, 16215, 45]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4260, 16475, F4, 44) (dual of [16475, 16215, 45]-code) | [i] | ||
| 3 | Linear OOA(4258, 8236, F4, 2, 44) (dual of [(8236, 2), 16214, 45]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(4258, 5491, F4, 3, 44) (dual of [(5491, 3), 16215, 45]-NRT-code) | [i] | ||