Information on Result #672248
Linear OA(2239, 2097201, F2, 23) (dual of [2097201, 2096962, 24]-code), using construction X applied to Ce(22) ⊂ Ce(18) based on
- linear OA(2232, 2097152, F2, 23) (dual of [2097152, 2096920, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2190, 2097152, F2, 19) (dual of [2097152, 2096962, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(27, 49, F2, 3) (dual of [49, 42, 4]-code or 49-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(2239, 2097201, F2, 22) (dual of [2097201, 2096962, 23]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2240, 2097202, F2, 23) (dual of [2097202, 2096962, 24]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2241, 2097203, F2, 23) (dual of [2097203, 2096962, 24]-code) | [i] | ||
| 4 | Linear OA(2242, 2097204, F2, 23) (dual of [2097204, 2096962, 24]-code) | [i] | ||
| 5 | Linear OA(2238, 2097200, F2, 22) (dual of [2097200, 2096962, 23]-code) | [i] | Truncation | |
| 6 | Linear OOA(2239, 1048600, F2, 2, 23) (dual of [(1048600, 2), 2096961, 24]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(2239, 699067, F2, 3, 23) (dual of [(699067, 3), 2096962, 24]-NRT-code) | [i] | ||
| 8 | Linear OOA(2239, 524300, F2, 4, 23) (dual of [(524300, 4), 2096961, 24]-NRT-code) | [i] | ||
| 9 | Linear OOA(2239, 419440, F2, 5, 23) (dual of [(419440, 5), 2096961, 24]-NRT-code) | [i] | ||
| 10 | Linear OOA(2239, 349533, F2, 6, 23) (dual of [(349533, 6), 2096959, 24]-NRT-code) | [i] | ||
| 11 | Linear OOA(2239, 299600, F2, 7, 23) (dual of [(299600, 7), 2096961, 24]-NRT-code) | [i] | ||
| 12 | Linear OOA(2239, 262150, F2, 8, 23) (dual of [(262150, 8), 2096961, 24]-NRT-code) | [i] | ||
| 13 | Linear OOA(2239, 190654, F2, 23, 23) (dual of [(190654, 23), 4384803, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |