Information on Result #1297599
Linear OA(2240, 568, F2, 52) (dual of [568, 328, 53]-code), using construction X with Varšamov bound based on
- linear OA(2229, 551, F2, 52) (dual of [551, 322, 53]-code), using
- construction XX applied to C1 = C([461,510]), C2 = C([467,2]), C3 = C1 + C2 = C([467,510]), 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(2199, 511, F2, 47) (dual of [511, 312, 48]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−44,−43,…,2}, and designed minimum distance d ≥ |I|+1 = 48 [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(2189, 511, F2, 44) (dual of [511, 322, 45]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−44,−43,…,−1}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(211, 29, F2, 5) (dual of [29, 18, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), 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([461,510]), C2 = C([467,2]), C3 = C1 + C2 = C([467,510]), and C∩ = C1 ∩ C2 = C([461,2]) [i] based on
- linear OA(2229, 557, F2, 48) (dual of [557, 328, 49]-code), using Gilbert–Varšamov bound and bm = 2229 > Vbs−1(k−1) = 600 873685 361236 993757 948283 731004 026174 139528 975109 262425 837642 837632 [i]
- linear OA(25, 11, F2, 3) (dual of [11, 6, 4]-code or 11-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
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.