Information on Result #700561
Linear OA(231, 144, F2, 8) (dual of [144, 113, 9]-code), using construction XX applied to C1 = C({0,1,3,63}), C2 = C([1,5]), C3 = C1 + C2 = C([1,3]), and C∩ = C1 ∩ C2 = C({0,1,3,5,63}) based on
- linear OA(222, 127, F2, 7) (dual of [127, 105, 8]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,63}, and minimum distance d ≥ |{−2,−1,…,4}|+1 = 8 (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(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(214, 127, F2, 4) (dual of [127, 113, 5]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 5 [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.
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Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(231, 89, F2, 2, 8) (dual of [(89, 2), 147, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(231, 89, F2, 3, 8) (dual of [(89, 3), 236, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(231, 89, F2, 4, 8) (dual of [(89, 4), 325, 9]-NRT-code) | [i] | ||
| 4 | Linear OOA(231, 89, F2, 5, 8) (dual of [(89, 5), 414, 9]-NRT-code) | [i] | ||
| 5 | Linear OOA(231, 89, F2, 6, 8) (dual of [(89, 6), 503, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(231, 89, F2, 7, 8) (dual of [(89, 7), 592, 9]-NRT-code) | [i] | ||
| 7 | Linear OA(232, 145, F2, 9) (dual of [145, 113, 10]-code) | [i] | Adding a Parity Check Bit | |
| 8 | Linear OOA(231, 72, F2, 2, 8) (dual of [(72, 2), 113, 9]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(231, 48, F2, 3, 8) (dual of [(48, 3), 113, 9]-NRT-code) | [i] | ||
| 10 | Linear OOA(231, 36, F2, 4, 8) (dual of [(36, 4), 113, 9]-NRT-code) | [i] | ||