Information on Result #737299
Linear OA(4213, 4165, F4, 43) (dual of [4165, 3952, 44]-code), using construction X applied to C([0,21]) ⊂ C([0,16]) based on
- linear OA(4193, 4097, F4, 43) (dual of [4097, 3904, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(4145, 4097, F4, 33) (dual of [4097, 3952, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (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(4214, 4166, F4, 43) (dual of [4166, 3952, 44]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4216, 4168, F4, 43) (dual of [4168, 3952, 44]-code) | [i] | ||
| 3 | Linear OA(4217, 4169, F4, 43) (dual of [4169, 3952, 44]-code) | [i] | ||
| 4 | Linear OA(4218, 4170, F4, 43) (dual of [4170, 3952, 44]-code) | [i] | ||
| 5 | Linear OA(4219, 4171, F4, 43) (dual of [4171, 3952, 44]-code) | [i] | ||
| 6 | Linear OA(4220, 4172, F4, 43) (dual of [4172, 3952, 44]-code) | [i] | ||
| 7 | Linear OOA(4213, 2082, F4, 2, 43) (dual of [(2082, 2), 3951, 44]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(4213, 1388, F4, 3, 43) (dual of [(1388, 3), 3951, 44]-NRT-code) | [i] | ||