Information on Result #737350
Linear OA(4211, 4168, F4, 42) (dual of [4168, 3957, 43]-code), using construction X applied to Ce(41) ⊂ Ce(30) based on
- linear OA(4187, 4096, F4, 42) (dual of [4096, 3909, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(4139, 4096, F4, 31) (dual of [4096, 3957, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(424, 72, F4, 10) (dual of [72, 48, 11]-code), using
- construction XX applied to C1 = C({0,1,2,3,5,6,47}), C2 = C([1,7]), C3 = C1 + C2 = C([1,6]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,47}) [i] based on
- linear OA(419, 63, F4, 8) (dual of [63, 44, 9]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,47}, and minimum distance d ≥ |{−1,0,…,6}|+1 = 9 (BCH-bound) [i]
- linear OA(418, 63, F4, 8) (dual of [63, 45, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(422, 63, F4, 10) (dual of [63, 41, 11]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,47}, and minimum distance d ≥ |{−1,0,…,8}|+1 = 11 (BCH-bound) [i]
- linear OA(415, 63, F4, 6) (dual of [63, 48, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(41, 5, F4, 1) (dual of [5, 4, 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(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
- construction XX applied to C1 = C({0,1,2,3,5,6,47}), C2 = C([1,7]), C3 = C1 + C2 = C([1,6]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,47}) [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(4212, 4169, F4, 42) (dual of [4169, 3957, 43]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4214, 4171, F4, 42) (dual of [4171, 3957, 43]-code) | [i] | ||
| 3 | Linear OOA(4211, 2084, F4, 2, 42) (dual of [(2084, 2), 3957, 43]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(4211, 1389, F4, 3, 42) (dual of [(1389, 3), 3956, 43]-NRT-code) | [i] | ||