Information on Result #700602
Linear OA(276, 160, F2, 21) (dual of [160, 84, 22]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,63}), C2 = C([0,15]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,63}) 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 = {0,1,3,5,7,9,11,63}, and minimum distance d ≥ |{−2,−1,…,12}|+1 = 16 (BCH-bound) [i]
- linear OA(257, 127, F2, 19) (dual of [127, 70, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(264, 127, F2, 21) (dual of [127, 63, 22]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,63}, and minimum distance d ≥ |{−2,−1,…,18}|+1 = 22 (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(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
- linear OA(211, 25, F2, 5) (dual of [25, 14, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), 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(275, 159, F2, 20) (dual of [159, 84, 21]-code) | [i] | Truncation | |
| 2 | Linear OOA(276, 80, F2, 2, 21) (dual of [(80, 2), 84, 22]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(276, 53, F2, 3, 21) (dual of [(53, 3), 83, 22]-NRT-code) | [i] | ||