Information on Result #1297535
Linear OA(2258, 311, F2, 88) (dual of [311, 53, 89]-code), using construction X with Varšamov bound based on
- linear OA(2221, 268, F2, 88) (dual of [268, 47, 89]-code), using
- construction XX applied to C1 = C([251,84]), C2 = C([1,86]), C3 = C1 + C2 = C([1,84]), and C∩ = C1 ∩ C2 = C([251,86]) [i] based on
- linear OA(2217, 255, F2, 89) (dual of [255, 38, 90]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,84}, and designed minimum distance d ≥ |I|+1 = 90 [i]
- linear OA(2210, 255, F2, 86) (dual of [255, 45, 87]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,86], and designed minimum distance d ≥ |I|+1 = 87 [i]
- linear OA(2219, 255, F2, 91) (dual of [255, 36, 92]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,86}, and designed minimum distance d ≥ |I|+1 = 92 [i]
- linear OA(2208, 255, F2, 84) (dual of [255, 47, 85]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,84], and designed minimum distance d ≥ |I|+1 = 85 [i]
- 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
- 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)
- construction XX applied to C1 = C([251,84]), C2 = C([1,86]), C3 = C1 + C2 = C([1,84]), and C∩ = C1 ∩ C2 = C([251,86]) [i] based on
- linear OA(2221, 274, F2, 71) (dual of [274, 53, 72]-code), using Gilbert–Varšamov bound and bm = 2221 > Vbs−1(k−1) = 2 608067 102532 121513 673086 224370 444752 438706 054140 484969 735752 532408 [i]
- linear OA(231, 37, F2, 16) (dual of [37, 6, 17]-code), using
- 1 times truncation [i] based on linear OA(232, 38, F2, 17) (dual of [38, 6, 18]-code), using
- construction X applied to Ce(30) ⊂ Ce(14) [i] based on
- linear OA(231, 32, F2, 31) (dual of [32, 1, 32]-code or 32-arc in PG(30,2)), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(226, 32, F2, 15) (dual of [32, 6, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(21, 6, F2, 1) (dual of [6, 5, 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)
- construction X applied to Ce(30) ⊂ Ce(14) [i] based on
- 1 times truncation [i] based on linear OA(232, 38, F2, 17) (dual of [38, 6, 18]-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(2259, 312, F2, 89) (dual of [312, 53, 90]-code) | [i] | Adding a Parity Check Bit | |