Information on Result #1297245
Linear OA(2128, 158, F2, 48) (dual of [158, 30, 49]-code), using construction X with Varšamov bound based on
- linear OA(2119, 148, F2, 48) (dual of [148, 29, 49]-code), using
- construction XX applied to C1 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,63}), C2 = C([1,43]), C3 = C1 + C2 = C([1,31]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,63}) [i] based on
- linear OA(2106, 127, F2, 47) (dual of [127, 21, 48]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,63}, and minimum distance d ≥ |{−4,−3,…,42}|+1 = 48 (BCH-bound) [i]
- linear OA(2105, 127, F2, 46) (dual of [127, 22, 47]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(2113, 127, F2, 51) (dual of [127, 14, 52]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,63}, and minimum distance d ≥ |{−4,−3,…,46}|+1 = 52 (BCH-bound) [i]
- linear OA(298, 127, F2, 42) (dual of [127, 29, 43]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [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(25, 12, F2, 3) (dual of [12, 7, 4]-code or 12-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
- construction XX applied to C1 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,63}), C2 = C([1,43]), C3 = C1 + C2 = C([1,31]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,63}) [i] based on
- linear OA(2119, 149, F2, 39) (dual of [149, 30, 40]-code), using Gilbert–Varšamov bound and bm = 2119 > Vbs−1(k−1) = 463780 416056 472996 395628 279451 282448 [i]
- linear OA(28, 9, F2, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,2)), using
- dual of repetition code with length 9 [i]
Mode: 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 OA(2129, 159, F2, 49) (dual of [159, 30, 50]-code) | [i] | Adding a Parity Check Bit | |