Information on Result #1297639
Linear OA(2244, 577, F2, 52) (dual of [577, 333, 53]-code), using construction X with Varšamov bound based on
- linear OA(2237, 564, F2, 52) (dual of [564, 327, 53]-code), using
- construction XX applied to C1 = C([461,510]), C2 = C([469,2]), C3 = C1 + C2 = C([469,510]), and C∩ = C1 ∩ C2 = C([461,2]) [i] based on
- linear OA(2207, 511, F2, 50) (dual of [511, 304, 51]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−50,−49,…,−1}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2190, 511, F2, 45) (dual of [511, 321, 46]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−42,−41,…,2}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2217, 511, F2, 53) (dual of [511, 294, 54]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−50,−49,…,2}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(2180, 511, F2, 42) (dual of [511, 331, 43]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−42,−41,…,−1}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(216, 39, F2, 6) (dual of [39, 23, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(216, 42, F2, 6) (dual of [42, 26, 7]-code), using
- extracting embedded orthogonal array [i] based on digital (10, 16, 42)-net over F2, using
- discarding factors / shortening the dual code based on linear OA(216, 42, F2, 6) (dual of [42, 26, 7]-code), using
- linear OA(24, 14, F2, 2) (dual of [14, 10, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(24, 15, F2, 2) (dual of [15, 11, 3]-code), using
- Hamming code H(4,2) [i]
- discarding factors / shortening the dual code based on linear OA(24, 15, F2, 2) (dual of [15, 11, 3]-code), using
- construction XX applied to C1 = C([461,510]), C2 = C([469,2]), C3 = C1 + C2 = C([469,510]), and C∩ = C1 ∩ C2 = C([461,2]) [i] based on
- linear OA(2237, 570, F2, 50) (dual of [570, 333, 51]-code), using Gilbert–Varšamov bound and bm = 2237 > Vbs−1(k−1) = 216245 399185 415737 829185 922337 435375 923376 721594 891250 798812 726813 026514 [i]
- linear OA(21, 7, F2, 1) (dual of [7, 6, 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
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
None.