Information on Result #809454
Linear OOA(2259, 546, F2, 2, 49) (dual of [(546, 2), 833, 50]-NRT-code), using OOA 2-folding based on linear OA(2259, 1092, F2, 49) (dual of [1092, 833, 50]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2258, 1091, F2, 49) (dual of [1091, 833, 50]-code), using
- adding a parity check bit [i] based on linear OA(2257, 1090, F2, 48) (dual of [1090, 833, 49]-code), using
- construction XX applied to C1 = C([979,1022]), C2 = C([985,4]), C3 = C1 + C2 = C([985,1022]), and C∩ = C1 ∩ C2 = C([979,4]) [i] based on
- linear OA(2215, 1023, F2, 44) (dual of [1023, 808, 45]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−44,−43,…,−1}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2206, 1023, F2, 43) (dual of [1023, 817, 44]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−38,−37,…,4}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2236, 1023, F2, 49) (dual of [1023, 787, 50]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−44,−43,…,4}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2185, 1023, F2, 38) (dual of [1023, 838, 39]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−38,−37,…,−1}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(211, 36, F2, 4) (dual of [36, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(211, 44, F2, 4) (dual of [44, 33, 5]-code), using
- linear OA(210, 31, F2, 4) (dual of [31, 21, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 32, F2, 4) (dual of [32, 22, 5]-code), using
- 1 times truncation [i] based on linear OA(211, 33, F2, 5) (dual of [33, 22, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33 | 210−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(211, 33, F2, 5) (dual of [33, 22, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 32, F2, 4) (dual of [32, 22, 5]-code), using
- construction XX applied to C1 = C([979,1022]), C2 = C([985,4]), C3 = C1 + C2 = C([985,1022]), and C∩ = C1 ∩ C2 = C([979,4]) [i] based on
- adding a parity check bit [i] based on linear OA(2257, 1090, F2, 48) (dual of [1090, 833, 49]-code), using
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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2258, 545, F2, 2, 48) (dual of [(545, 2), 832, 49]-NRT-code) | [i] | Truncation for OOAs | |