Information on Result #700530
Linear OA(236, 74, F2, 13) (dual of [74, 38, 14]-code), using construction XX applied to C1 = C({0,1,3,5,7,31}), C2 = C([0,9]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,31}) based on
- linear OA(231, 63, F2, 11) (dual of [63, 32, 12]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,1,3,5,7,31}, and minimum distance d ≥ |{−2,−1,…,8}|+1 = 12 (BCH-bound) [i]
- linear OA(228, 63, F2, 11) (dual of [63, 35, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(234, 63, F2, 13) (dual of [63, 29, 14]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,1,3,5,7,9,31}, and minimum distance d ≥ |{−2,−1,…,10}|+1 = 14 (BCH-bound) [i]
- linear OA(225, 63, F2, 9) (dual of [63, 38, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 10 [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, 4, F2, 1) (dual of [4, 3, 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(235, 73, F2, 12) (dual of [73, 38, 13]-code) | [i] | Truncation | |
| 2 | Linear OOA(236, 37, F2, 2, 13) (dual of [(37, 2), 38, 14]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(236, 24, F2, 3, 13) (dual of [(24, 3), 36, 14]-NRT-code) | [i] | ||