Information on Result #700544
Linear OA(256, 73, F2, 25) (dual of [73, 17, 26]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,13,15,31}), C2 = C([0,21]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,21,31}) based on
- linear OA(252, 63, F2, 25) (dual of [63, 11, 26]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,1,3,5,7,9,11,13,15,31}, and minimum distance d ≥ |{−4,−3,…,20}|+1 = 26 (BCH-bound) [i]
- linear OA(248, 63, F2, 23) (dual of [63, 15, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(254, 63, F2, 27) (dual of [63, 9, 28]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,1,3,5,7,9,11,13,15,21,31}, and minimum distance d ≥ |{−4,−3,…,22}|+1 = 28 (BCH-bound) [i]
- linear OA(246, 63, F2, 21) (dual of [63, 17, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(21, 7, F2, 1) (dual of [7, 6, 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
- 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 (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(255, 72, F2, 24) (dual of [72, 17, 25]-code) | [i] | Truncation | |
| 2 | Linear OOA(256, 36, F2, 2, 25) (dual of [(36, 2), 16, 26]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(256, 24, F2, 3, 25) (dual of [(24, 3), 16, 26]-NRT-code) | [i] | ||