Information on Result #1304000
Linear OA(2243, 579, F2, 52) (dual of [579, 336, 53]-code), using 15 step Varšamov–Edel lengthening with (ri) = (4, 2, 2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0) based on linear OA(2228, 549, F2, 52) (dual of [549, 321, 53]-code), using
- 1 times truncation [i] based on linear OA(2229, 550, F2, 53) (dual of [550, 321, 54]-code), using
- construction XX applied to C1 = C([461,0]), C2 = C([467,2]), C3 = C1 + C2 = C([467,0]), and C∩ = C1 ∩ C2 = C([461,2]) [i] based on
- linear OA(2208, 511, F2, 51) (dual of [511, 303, 52]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−50,−49,…,0}, and designed minimum distance d ≥ |I|+1 = 52 [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(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 = {−44,−43,…,0}, and designed minimum distance d ≥ |I|+1 = 46 [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, 10, F2, 1) (dual of [10, 9, 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([461,0]), C2 = C([467,2]), C3 = C1 + C2 = C([467,0]), and C∩ = C1 ∩ C2 = C([461,2]) [i] based on
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 OA(2244, 580, F2, 53) (dual of [580, 336, 54]-code) | [i] | Adding a Parity Check Bit | |