Information on Result #700566
Linear OA(238, 144, F2, 10) (dual of [144, 106, 11]-code), using construction XX applied to C1 = C({0,1,3,5,63}), C2 = C([1,7]), C3 = C1 + C2 = C([1,5]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,63}) based on
- linear OA(229, 127, F2, 9) (dual of [127, 98, 10]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,63}, and minimum distance d ≥ |{−2,−1,…,6}|+1 = 10 (BCH-bound) [i]
- linear OA(228, 127, F2, 8) (dual of [127, 99, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(236, 127, F2, 11) (dual of [127, 91, 12]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,63}, and minimum distance d ≥ |{−2,−1,…,8}|+1 = 12 (BCH-bound) [i]
- linear OA(221, 127, F2, 6) (dual of [127, 106, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(21, 9, F2, 1) (dual of [9, 8, 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, 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 (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 OOA(238, 84, F2, 2, 10) (dual of [(84, 2), 130, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(238, 84, F2, 3, 10) (dual of [(84, 3), 214, 11]-NRT-code) | [i] | ||
| 3 | Linear OOA(238, 84, F2, 4, 10) (dual of [(84, 4), 298, 11]-NRT-code) | [i] | ||
| 4 | Linear OOA(238, 84, F2, 5, 10) (dual of [(84, 5), 382, 11]-NRT-code) | [i] | ||
| 5 | Linear OOA(238, 84, F2, 6, 10) (dual of [(84, 6), 466, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(238, 84, F2, 7, 10) (dual of [(84, 7), 550, 11]-NRT-code) | [i] | ||
| 7 | Linear OOA(238, 84, F2, 8, 10) (dual of [(84, 8), 634, 11]-NRT-code) | [i] | ||
| 8 | Digital (28, 38, 84)-net over F2 | [i] | ||
| 9 | Linear OA(239, 145, F2, 11) (dual of [145, 106, 12]-code) | [i] | Adding a Parity Check Bit | |
| 10 | Linear OOA(238, 72, F2, 2, 10) (dual of [(72, 2), 106, 11]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(238, 48, F2, 3, 10) (dual of [(48, 3), 106, 11]-NRT-code) | [i] | ||
| 12 | Linear OOA(238, 36, F2, 4, 10) (dual of [(36, 4), 106, 11]-NRT-code) | [i] | ||