Information on Result #672478
Linear OA(2195, 131113, F2, 23) (dual of [131113, 130918, 24]-code), using construction X applied to Ce(22) ⊂ Ce(18) based on
- linear OA(2188, 131072, F2, 23) (dual of [131072, 130884, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2154, 131072, F2, 19) (dual of [131072, 130918, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(27, 41, F2, 3) (dual of [41, 34, 4]-code or 41-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), 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(2195, 131113, F2, 22) (dual of [131113, 130918, 23]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2196, 131114, F2, 23) (dual of [131114, 130918, 24]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2197, 131115, F2, 23) (dual of [131115, 130918, 24]-code) | [i] | ||
| 4 | Linear OA(2198, 131116, F2, 23) (dual of [131116, 130918, 24]-code) | [i] | ||
| 5 | Linear OA(2194, 131112, F2, 22) (dual of [131112, 130918, 23]-code) | [i] | Truncation | |
| 6 | Linear OOA(2195, 65556, F2, 2, 23) (dual of [(65556, 2), 130917, 24]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(2195, 43704, F2, 3, 23) (dual of [(43704, 3), 130917, 24]-NRT-code) | [i] | ||
| 8 | Linear OOA(2195, 32778, F2, 4, 23) (dual of [(32778, 4), 130917, 24]-NRT-code) | [i] | ||
| 9 | Linear OOA(2195, 26222, F2, 5, 23) (dual of [(26222, 5), 130915, 24]-NRT-code) | [i] | ||
| 10 | Linear OOA(2195, 21852, F2, 6, 23) (dual of [(21852, 6), 130917, 24]-NRT-code) | [i] | ||
| 11 | Linear OOA(2195, 18730, F2, 7, 23) (dual of [(18730, 7), 130915, 24]-NRT-code) | [i] | ||
| 12 | Linear OOA(2195, 16389, F2, 8, 23) (dual of [(16389, 8), 130917, 24]-NRT-code) | [i] | ||
| 13 | Linear OOA(2195, 11919, F2, 23, 23) (dual of [(11919, 23), 273942, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |