Information on Result #1589524
Linear OOA(284, 431, F2, 4, 16) (dual of [(431, 4), 1640, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(284, 431, F2, 2, 16) (dual of [(431, 2), 778, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(284, 523, F2, 2, 16) (dual of [(523, 2), 962, 17]-NRT-code), using
- strength reduction [i] based on linear OOA(284, 523, F2, 2, 17) (dual of [(523, 2), 962, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(284, 1046, F2, 17) (dual of [1046, 962, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(284, 1047, F2, 17) (dual of [1047, 963, 18]-code), using
- adding a parity check bit [i] based on linear OA(283, 1046, F2, 16) (dual of [1046, 963, 17]-code), using
- construction XX applied to C1 = C([1021,12]), C2 = C([1,14]), C3 = C1 + C2 = C([1,12]), and C∩ = C1 ∩ C2 = C([1021,14]) [i] based on
- linear OA(271, 1023, F2, 15) (dual of [1023, 952, 16]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,12}, and designed minimum distance d ≥ |I|+1 = 16 [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(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 = {−2,−1,…,14}, and designed minimum distance d ≥ |I|+1 = 18 [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(21, 12, F2, 1) (dual of [12, 11, 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, 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 (see above)
- construction XX applied to C1 = C([1021,12]), C2 = C([1,14]), C3 = C1 + C2 = C([1,12]), and C∩ = C1 ∩ C2 = C([1021,14]) [i] based on
- adding a parity check bit [i] based on linear OA(283, 1046, F2, 16) (dual of [1046, 963, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(284, 1047, F2, 17) (dual of [1047, 963, 18]-code), using
- OOA 2-folding [i] based on linear OA(284, 1046, F2, 17) (dual of [1046, 962, 18]-code), using
- strength reduction [i] based on linear OOA(284, 523, F2, 2, 17) (dual of [(523, 2), 962, 18]-NRT-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(284, 215, F2, 7, 16) (dual of [(215, 7), 1421, 17]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(284, 215, F2, 8, 16) (dual of [(215, 8), 1636, 17]-NRT-code) | [i] | ||