Information on Result #640795
Linear OA(2218, 234, F2, 98) (dual of [234, 16, 99]-code), using juxtaposition based on
- linear OA(223, 39, F2, 10) (dual of [39, 16, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(223, 47, F2, 10) (dual of [47, 24, 11]-code), using
- 1 times truncation [i] based on linear OA(224, 48, F2, 11) (dual of [48, 24, 12]-code), using
- extended quadratic residue code Qe(48,2) [i]
- 1 times truncation [i] based on linear OA(224, 48, F2, 11) (dual of [48, 24, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(223, 47, F2, 10) (dual of [47, 24, 11]-code), using
- linear OA(2179, 195, F2, 87) (dual of [195, 16, 88]-code), using
- concatenation of two codes [i] based on
- linear OA(457, 65, F4, 43) (dual of [65, 8, 44]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(21, 3, F2, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(457, 65, F4, 43) (dual of [65, 8, 44]-code), using
- concatenation of two codes [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.
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 OA(2218, 234, F2, 97) (dual of [234, 16, 98]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2218, 234, F2, 96) (dual of [234, 16, 97]-code) | [i] | ||
| 3 | Linear OA(2218, 234, F2, 95) (dual of [234, 16, 96]-code) | [i] | ||
| 4 | Linear OA(2219, 235, F2, 99) (dual of [235, 16, 100]-code) | [i] | Adding a Parity Check Bit | |