Information on Result #1297270
Linear OA(2151, 283, F2, 40) (dual of [283, 132, 41]-code), using construction X with Varšamov bound based on
- linear OA(2142, 272, F2, 40) (dual of [272, 130, 41]-code), using
- 1 times truncation [i] based on linear OA(2143, 273, F2, 41) (dual of [273, 130, 42]-code), using
- construction XX applied to C1 = C([253,36]), C2 = C([0,38]), C3 = C1 + C2 = C([0,36]), and C∩ = C1 ∩ C2 = C([253,38]) [i] based on
- linear OA(2133, 255, F2, 39) (dual of [255, 122, 40]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,36}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2133, 255, F2, 39) (dual of [255, 122, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2141, 255, F2, 41) (dual of [255, 114, 42]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,38}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2125, 255, F2, 37) (dual of [255, 130, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(21, 9, F2, 1) (dual of [9, 8, 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, 9, F2, 1) (dual of [9, 8, 2]-code) (see above)
- construction XX applied to C1 = C([253,36]), C2 = C([0,38]), C3 = C1 + C2 = C([0,36]), and C∩ = C1 ∩ C2 = C([253,38]) [i] based on
- 1 times truncation [i] based on linear OA(2143, 273, F2, 41) (dual of [273, 130, 42]-code), using
- linear OA(2142, 274, F2, 34) (dual of [274, 132, 35]-code), using Gilbert–Varšamov bound and bm = 2142 > Vbs−1(k−1) = 4 393821 395201 179987 229462 394138 077510 153008 [i]
- linear OA(27, 9, F2, 5) (dual of [9, 2, 6]-code), using
- repeating each code word 3 times [i] based on linear OA(21, 3, F2, 1) (dual of [3, 2, 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)
- repeating each code word 3 times [i] based on linear OA(21, 3, F2, 1) (dual of [3, 2, 2]-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 OA(2152, 284, F2, 41) (dual of [284, 132, 42]-code) | [i] | Adding a Parity Check Bit | |