Information on Result #674057
Linear OA(2123, 153, F2, 47) (dual of [153, 30, 48]-code), using construction XX applied to Ce(46) ⊂ Ce(42) ⊂ Ce(30) based on
- linear OA(2106, 128, F2, 47) (dual of [128, 22, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(299, 128, F2, 43) (dual of [128, 29, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(292, 128, F2, 31) (dual of [128, 36, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(25, 13, F2, 3) (dual of [13, 8, 4]-code or 13-cap in PG(4,2)), using
- discarding factors / shortening the dual code based on linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
- linear OA(211, 12, F2, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,2)), using
- dual of repetition code with length 12 [i]
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(2123, 153, F2, 46) (dual of [153, 30, 47]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2123, 153, F2, 45) (dual of [153, 30, 46]-code) | [i] | ||
| 3 | Linear OA(2122, 152, F2, 46) (dual of [152, 30, 47]-code) | [i] | Truncation | |
| 4 | Linear OA(2120, 150, F2, 44) (dual of [150, 30, 45]-code) | [i] | ||
| 5 | Linear OOA(2123, 51, F2, 3, 47) (dual of [(51, 3), 30, 48]-NRT-code) | [i] | OOA Folding | |