Information on Result #731717
Linear OA(2194, 210, F2, 91) (dual of [210, 16, 92]-code), using concatenation of two codes based on
- linear OA(462, 70, F4, 45) (dual of [70, 8, 46]-code), using
- construction XX applied to Ce(46) ⊂ Ce(42) ⊂ Ce(41) [i] based on
- linear OA(460, 64, F4, 47) (dual of [64, 4, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(457, 64, F4, 43) (dual of [64, 7, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(456, 64, F4, 42) (dual of [64, 8, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [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(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(46) ⊂ Ce(42) ⊂ Ce(41) [i] based on
- 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
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(2194, 210, F2, 90) (dual of [210, 16, 91]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2194, 210, F2, 89) (dual of [210, 16, 90]-code) | [i] | ||
| 3 | Linear OA(2194, 210, F2, 88) (dual of [210, 16, 89]-code) | [i] | ||
| 4 | Linear OA(2193, 209, F2, 90) (dual of [209, 16, 91]-code) | [i] | Truncation | |
| 5 | Linear OA(2192, 208, F2, 89) (dual of [208, 16, 90]-code) | [i] | ||
| 6 | Linear OA(2190, 206, F2, 87) (dual of [206, 16, 88]-code) | [i] | ||
| 7 | Linear OA(2189, 205, F2, 86) (dual of [205, 16, 87]-code) | [i] | ||
| 8 | Linear OA(2188, 204, F2, 85) (dual of [204, 16, 86]-code) | [i] | ||
| 9 | Linear OA(2187, 203, F2, 84) (dual of [203, 16, 85]-code) | [i] | ||
| 10 | Linear OA(2186, 202, F2, 83) (dual of [202, 16, 84]-code) | [i] | ||
| 11 | Linear OA(2185, 201, F2, 82) (dual of [201, 16, 83]-code) | [i] | ||
| 12 | Linear OA(2184, 200, F2, 81) (dual of [200, 16, 82]-code) | [i] | ||
| 13 | Linear OA(2183, 199, F2, 80) (dual of [199, 16, 81]-code) | [i] | ||
| 14 | Linear OA(2182, 198, F2, 79) (dual of [198, 16, 80]-code) | [i] | ||
| 15 | Linear OA(2181, 197, F2, 78) (dual of [197, 16, 79]-code) | [i] | ||
| 16 | Linear OOA(2194, 105, F2, 2, 91) (dual of [(105, 2), 16, 92]-NRT-code) | [i] | OOA Folding | |
| 17 | Linear OOA(2194, 70, F2, 3, 91) (dual of [(70, 3), 16, 92]-NRT-code) | [i] | ||
| 18 | Linear OOA(2194, 42, F2, 5, 91) (dual of [(42, 5), 16, 92]-NRT-code) | [i] | ||