Information on Result #2220375
Linear OA(263, 154, F2, 16) (dual of [154, 91, 17]-code), using 1 times truncation based on linear OA(264, 155, F2, 17) (dual of [155, 91, 18]-code), using
- construction XX applied to C1 = C({0,1,3,5,7,9,31,63}), C2 = C([0,11]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,31,63}) [i] based on
- linear OA(250, 127, F2, 15) (dual of [127, 77, 16]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,31,63}, and minimum distance d ≥ |{−4,−3,…,10}|+1 = 16 (BCH-bound) [i]
- linear OA(243, 127, F2, 13) (dual of [127, 84, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(257, 127, F2, 17) (dual of [127, 70, 18]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,31,63}, and minimum distance d ≥ |{−4,−3,…,12}|+1 = 18 (BCH-bound) [i]
- linear OA(236, 127, F2, 11) (dual of [127, 91, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(26, 20, F2, 3) (dual of [20, 14, 4]-code or 20-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- linear OA(21, 8, F2, 1) (dual of [8, 7, 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
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 OOA(263, 77, F2, 2, 16) (dual of [(77, 2), 91, 17]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(263, 51, F2, 3, 16) (dual of [(51, 3), 90, 17]-NRT-code) | [i] | ||