Information on Result #673459
Linear OA(2153, 531, F2, 35) (dual of [531, 378, 36]-code), using construction XX applied to Ce(34) ⊂ Ce(30) ⊂ Ce(28) based on
- linear OA(2145, 512, F2, 35) (dual of [512, 367, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2136, 512, F2, 31) (dual of [512, 376, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2127, 512, F2, 29) (dual of [512, 385, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
- 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(2153, 531, F2, 34) (dual of [531, 378, 35]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2154, 532, F2, 35) (dual of [532, 378, 36]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2152, 530, F2, 34) (dual of [530, 378, 35]-code) | [i] | Truncation | |
| 4 | Linear OOA(2153, 265, F2, 2, 35) (dual of [(265, 2), 377, 36]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2153, 177, F2, 3, 35) (dual of [(177, 3), 378, 36]-NRT-code) | [i] | ||
| 6 | Linear OOA(2153, 106, F2, 5, 35) (dual of [(106, 5), 377, 36]-NRT-code) | [i] | ||