Information on Result #2174987
Linear OA(2124, 153, F2, 51) (dual of [153, 29, 52]-code), using adding a parity check bit based on linear OA(2123, 152, F2, 50) (dual of [152, 29, 51]-code), using
- construction XX applied to C1 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,63}), C2 = C([1,43]), C3 = C1 + C2 = C([1,31]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,63}) [i] based on
- linear OA(2106, 127, F2, 47) (dual of [127, 21, 48]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,63}, and minimum distance d ≥ |{−4,−3,…,42}|+1 = 48 (BCH-bound) [i]
- linear OA(2105, 127, F2, 46) (dual of [127, 22, 47]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(2113, 127, F2, 51) (dual of [127, 14, 52]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,63}, and minimum distance d ≥ |{−4,−3,…,46}|+1 = 52 (BCH-bound) [i]
- linear OA(298, 127, F2, 42) (dual of [127, 29, 43]-code), using 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(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(25, 12, F2, 3) (dual of [12, 7, 4]-code or 12-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)) (see above)
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(2124, 153, F2, 50) (dual of [153, 29, 51]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2125, 154, F2, 51) (dual of [154, 29, 52]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2127, 156, F2, 51) (dual of [156, 29, 52]-code) | [i] | ||
| 4 | Linear OA(2128, 157, F2, 51) (dual of [157, 29, 52]-code) | [i] | ||
| 5 | Linear OA(2130, 159, F2, 51) (dual of [159, 29, 52]-code) | [i] | ||
| 6 | Linear OA(2122, 151, F2, 49) (dual of [151, 29, 50]-code) | [i] | Truncation | |
| 7 | Linear OA(2121, 150, F2, 48) (dual of [150, 29, 49]-code) | [i] | ||
| 8 | Linear OA(2118, 147, F2, 45) (dual of [147, 29, 46]-code) | [i] | ||
| 9 | Linear OA(2117, 146, F2, 44) (dual of [146, 29, 45]-code) | [i] | ||
| 10 | Linear OOA(2124, 76, F2, 2, 51) (dual of [(76, 2), 28, 52]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(2124, 51, F2, 3, 51) (dual of [(51, 3), 29, 52]-NRT-code) | [i] | ||