Information on Result #1589944
Linear OOA(299, 432, F2, 4, 19) (dual of [(432, 4), 1629, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(299, 432, F2, 2, 19) (dual of [(432, 2), 765, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(299, 531, F2, 2, 19) (dual of [(531, 2), 963, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(299, 1062, F2, 19) (dual of [1062, 963, 20]-code), using
- adding a parity check bit [i] based on linear OA(298, 1061, F2, 18) (dual of [1061, 963, 19]-code), using
- construction XX applied to C1 = C([1019,12]), C2 = C([1,14]), C3 = C1 + C2 = C([1,12]), and C∩ = C1 ∩ C2 = C([1019,14]) [i] based on
- linear OA(281, 1023, F2, 17) (dual of [1023, 942, 18]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,12}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(270, 1023, F2, 14) (dual of [1023, 953, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(291, 1023, F2, 19) (dual of [1023, 932, 20]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,14}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(260, 1023, F2, 12) (dual of [1023, 963, 13]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(26, 27, F2, 3) (dual of [27, 21, 4]-code or 27-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, 11, F2, 1) (dual of [11, 10, 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
- construction XX applied to C1 = C([1019,12]), C2 = C([1,14]), C3 = C1 + C2 = C([1,12]), and C∩ = C1 ∩ C2 = C([1019,14]) [i] based on
- adding a parity check bit [i] based on linear OA(298, 1061, F2, 18) (dual of [1061, 963, 19]-code), using
- OOA 2-folding [i] based on linear OA(299, 1062, F2, 19) (dual of [1062, 963, 20]-code), using
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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(299, 216, F2, 7, 19) (dual of [(216, 7), 1413, 20]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(299, 216, F2, 8, 19) (dual of [(216, 8), 1629, 20]-NRT-code) | [i] | ||