Information on Result #672552
Linear OA(2254, 65597, F2, 31) (dual of [65597, 65343, 32]-code), using construction X applied to Ce(30) ⊂ Ce(24) based on
- linear OA(2241, 65536, F2, 31) (dual of [65536, 65295, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2193, 65536, F2, 25) (dual of [65536, 65343, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(213, 61, F2, 5) (dual of [61, 48, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), 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(2254, 65597, F2, 30) (dual of [65597, 65343, 31]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2255, 65598, F2, 31) (dual of [65598, 65343, 32]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2253, 65596, F2, 30) (dual of [65596, 65343, 31]-code) | [i] | Truncation | |
| 4 | Linear OOA(2254, 32798, F2, 2, 31) (dual of [(32798, 2), 65342, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2254, 21865, F2, 3, 31) (dual of [(21865, 3), 65341, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(2254, 16399, F2, 4, 31) (dual of [(16399, 4), 65342, 32]-NRT-code) | [i] | ||
| 7 | Linear OOA(2254, 13119, F2, 5, 31) (dual of [(13119, 5), 65341, 32]-NRT-code) | [i] | ||
| 8 | Linear OOA(2254, 10932, F2, 6, 31) (dual of [(10932, 6), 65338, 32]-NRT-code) | [i] | ||
| 9 | Linear OOA(2254, 9371, F2, 7, 31) (dual of [(9371, 7), 65343, 32]-NRT-code) | [i] | ||
| 10 | Linear OOA(2254, 8199, F2, 8, 31) (dual of [(8199, 8), 65338, 32]-NRT-code) | [i] | ||
| 11 | Linear OOA(2254, 4373, F2, 31, 31) (dual of [(4373, 31), 135309, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |