Information on Result #2174878
Linear OA(237, 48, F2, 17) (dual of [48, 11, 18]-code), using adding a parity check bit based on linear OA(236, 47, F2, 16) (dual of [47, 11, 17]-code), using
- construction XX applied to C1 = C({1,3,5,7,15}), C2 = C([1,11]), C3 = C1 + C2 = C([1,7]), and C∩ = C1 ∩ C2 = C([1,15]) [i] based on
- linear OA(225, 31, F2, 14) (dual of [31, 6, 15]-code), using the primitive cyclic code C(A) with length 31 = 25−1, defining set A = {1,3,5,7,15}, and minimum distance d ≥ |{5,10,15,…,8}|+1 = 15 (BCH-bound) [i]
- linear OA(225, 31, F2, 14) (dual of [31, 6, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(230, 31, F2, 30) (dual of [31, 1, 31]-code or 31-arc in PG(29,2)), using the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(220, 31, F2, 10) (dual of [31, 11, 11]-code), using the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(21, 6, F2, 1) (dual of [6, 5, 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(25, 10, F2, 3) (dual of [10, 5, 4]-code or 10-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
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(237, 48, F2, 16) (dual of [48, 11, 17]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(238, 49, F2, 17) (dual of [49, 11, 18]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OOA(237, 24, F2, 2, 17) (dual of [(24, 2), 11, 18]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(237, 16, F2, 3, 17) (dual of [(16, 3), 11, 18]-NRT-code) | [i] | ||