Information on Result #547723

There is no linear OA(2247, 332, F2, 112) (dual of [332, 85, 113]-code), because construction Y1 would yield
  1. OA(2246, 302, S2, 112), but
    • 2 times truncation [i] would yield OA(2244, 300, S2, 110), but
      • the linear programming bound shows that M ≥ 727209 932038 995964 963694 786156 506719 769259 430085 807852 102717 045283 079365 167115 254635 995296 956416 / 21378 491075 472167 578125 > 2244 [i]
  2. linear OA(285, 332, F2, 30) (dual of [332, 247, 31]-code), but
    • the Johnson bound shows that N ≤ 220 247871 551638 926977 652794 793575 888633 238636 124356 543746 403131 692235 320146 < 2247 [i]

Mode: Bound (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:

ResultThis
result
only		Method
1No linear OA(2248, 333, F2, 113) (dual of [333, 85, 114]-code) [i]Truncation
2No linear OA(2249, 334, F2, 114) (dual of [334, 85, 115]-code) [i]
3No linear OA(2250, 335, F2, 115) (dual of [335, 85, 116]-code) [i]
4No linear OA(2251, 336, F2, 116) (dual of [336, 85, 117]-code) [i]
5No linear OA(2252, 337, F2, 117) (dual of [337, 85, 118]-code) [i]
6No linear OA(2253, 338, F2, 118) (dual of [338, 85, 119]-code) [i]
7No linear OA(2254, 339, F2, 119) (dual of [339, 85, 120]-code) [i]
8No linear OA(2255, 340, F2, 120) (dual of [340, 85, 121]-code) [i]
9No linear OA(2256, 341, F2, 121) (dual of [341, 85, 122]-code) [i]
10No linear OA(2257, 342, F2, 122) (dual of [342, 85, 123]-code) [i]
11No linear OA(2258, 343, F2, 123) (dual of [343, 85, 124]-code) [i]
12No linear OA(2259, 344, F2, 124) (dual of [344, 85, 125]-code) [i]
13No linear OA(2260, 345, F2, 125) (dual of [345, 85, 126]-code) [i]
14No linear OOA(2247, 332, F2, 2, 112) (dual of [(332, 2), 417, 113]-NRT-code) [i]Depth Reduction
15No linear OOA(2247, 332, F2, 3, 112) (dual of [(332, 3), 749, 113]-NRT-code) [i]
16No linear OOA(2247, 332, F2, 4, 112) (dual of [(332, 4), 1081, 113]-NRT-code) [i]
17No linear OOA(2247, 332, F2, 5, 112) (dual of [(332, 5), 1413, 113]-NRT-code) [i]
18No linear OOA(2247, 332, F2, 6, 112) (dual of [(332, 6), 1745, 113]-NRT-code) [i]
19No linear OOA(2247, 332, F2, 7, 112) (dual of [(332, 7), 2077, 113]-NRT-code) [i]
20No linear OOA(2247, 332, F2, 8, 112) (dual of [(332, 8), 2409, 113]-NRT-code) [i]
21No linear OA(2248, 384, F2, 112) (dual of [384, 136, 113]-code) [i]Construction Y1 (Bound)