Information on Result #737296
Linear OA(4249, 4165, F4, 51) (dual of [4165, 3916, 52]-code), using construction X applied to C([0,25]) ⊂ C([0,20]) based on
- linear OA(4229, 4097, F4, 51) (dual of [4097, 3868, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,25], and minimum distance d ≥ |{−25,−24,…,25}|+1 = 52 (BCH-bound) [i]
- linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(420, 68, F4, 9) (dual of [68, 48, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(419, 64, F4, 9) (dual of [64, 45, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using an extension Ce(6) of 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, 4, F4, 1) (dual of [4, 3, 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
- construction X applied to Ce(8) ⊂ Ce(6) [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(4250, 4166, F4, 51) (dual of [4166, 3916, 52]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4252, 4168, F4, 51) (dual of [4168, 3916, 52]-code) | [i] | ||
| 3 | Linear OA(4253, 4169, F4, 51) (dual of [4169, 3916, 52]-code) | [i] | ||
| 4 | Linear OA(4254, 4170, F4, 51) (dual of [4170, 3916, 52]-code) | [i] | ||
| 5 | Linear OA(4255, 4171, F4, 51) (dual of [4171, 3916, 52]-code) | [i] | ||
| 6 | Linear OA(4256, 4172, F4, 51) (dual of [4172, 3916, 52]-code) | [i] | ||
| 7 | Linear OOA(4249, 2082, F4, 2, 51) (dual of [(2082, 2), 3915, 52]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(4249, 1388, F4, 3, 51) (dual of [(1388, 3), 3915, 52]-NRT-code) | [i] | ||