Information on Result #2175194
Linear OA(2234, 2097176, F2, 23) (dual of [2097176, 2096942, 24]-code), using adding a parity check bit based on linear OA(2233, 2097175, F2, 22) (dual of [2097175, 2096942, 23]-code), using
- construction X4 applied to C([0,22]) ⊂ C([1,20]) [i] based on
- linear OA(2232, 2097151, F2, 23) (dual of [2097151, 2096919, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2210, 2097151, F2, 20) (dual of [2097151, 2096941, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(223, 24, F2, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,2)), using
- dual of repetition code with length 24 [i]
- linear OA(21, 24, F2, 1) (dual of [24, 23, 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
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(2234, 2097176, F2, 22) (dual of [2097176, 2096942, 23]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2235, 2097177, F2, 23) (dual of [2097177, 2096942, 24]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2236, 2097178, F2, 23) (dual of [2097178, 2096942, 24]-code) | [i] | ||
| 4 | Linear OA(2237, 2097179, F2, 23) (dual of [2097179, 2096942, 24]-code) | [i] | ||
| 5 | Linear OOA(2234, 1048588, F2, 2, 23) (dual of [(1048588, 2), 2096942, 24]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2234, 524294, F2, 4, 23) (dual of [(524294, 4), 2096942, 24]-NRT-code) | [i] | ||
| 7 | Linear OOA(2234, 419435, F2, 5, 23) (dual of [(419435, 5), 2096941, 24]-NRT-code) | [i] | ||
| 8 | Linear OOA(2234, 262147, F2, 8, 23) (dual of [(262147, 8), 2096942, 24]-NRT-code) | [i] | ||