Information on Result #700516
Linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4
Mode: Constructive and 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(2228, 4194356, F2, 21) (dual of [4194356, 4194128, 22]-code) | [i] | Construction X with Cyclic Codes | |
| 2 | Linear OA(2184, 4194356, F2, 17) (dual of [4194356, 4194172, 18]-code) | [i] | ||
| 3 | Linear OA(2260, 2097202, F2, 25) (dual of [2097202, 2096942, 26]-code) | [i] | ||
| 4 | Linear OA(2218, 2097202, F2, 21) (dual of [2097202, 2096984, 22]-code) | [i] | ||
| 5 | Linear OA(2176, 2097202, F2, 17) (dual of [2097202, 2097026, 18]-code) | [i] | ||
| 6 | Linear OA(2248, 1048624, F2, 25) (dual of [1048624, 1048376, 26]-code) | [i] | ||
| 7 | Linear OA(2208, 1048624, F2, 21) (dual of [1048624, 1048416, 22]-code) | [i] | ||
| 8 | Linear OA(2168, 1048624, F2, 17) (dual of [1048624, 1048456, 18]-code) | [i] | ||
| 9 | Linear OA(2236, 524334, F2, 25) (dual of [524334, 524098, 26]-code) | [i] | ||
| 10 | Linear OA(2198, 524334, F2, 21) (dual of [524334, 524136, 22]-code) | [i] | ||
| 11 | Linear OA(2160, 524334, F2, 17) (dual of [524334, 524174, 18]-code) | [i] | ||
| 12 | Linear OA(2260, 262188, F2, 29) (dual of [262188, 261928, 30]-code) | [i] | ||
| 13 | Linear OA(2224, 262188, F2, 25) (dual of [262188, 261964, 26]-code) | [i] | ||
| 14 | Linear OA(2188, 262188, F2, 21) (dual of [262188, 262000, 22]-code) | [i] | ||
| 15 | Linear OA(2152, 262188, F2, 17) (dual of [262188, 262036, 18]-code) | [i] | ||
| 16 | Linear OA(2246, 131114, F2, 29) (dual of [131114, 130868, 30]-code) | [i] | ||
| 17 | Linear OA(2212, 131114, F2, 25) (dual of [131114, 130902, 26]-code) | [i] | ||
| 18 | Linear OA(2178, 131114, F2, 21) (dual of [131114, 130936, 22]-code) | [i] | ||
| 19 | Linear OA(2144, 131114, F2, 17) (dual of [131114, 130970, 18]-code) | [i] | ||
| 20 | Linear OA(2232, 65576, F2, 29) (dual of [65576, 65344, 30]-code) | [i] | ||
| 21 | Linear OA(2200, 65576, F2, 25) (dual of [65576, 65376, 26]-code) | [i] | ||
| 22 | Linear OA(2168, 65576, F2, 21) (dual of [65576, 65408, 22]-code) | [i] | ||
| 23 | Linear OA(2136, 65576, F2, 17) (dual of [65576, 65440, 18]-code) | [i] | ||
| 24 | Linear OA(2248, 32806, F2, 33) (dual of [32806, 32558, 34]-code) | [i] | ||
| 25 | Linear OA(2218, 32806, F2, 29) (dual of [32806, 32588, 30]-code) | [i] | ||
| 26 | Linear OA(2188, 32806, F2, 25) (dual of [32806, 32618, 26]-code) | [i] | ||
| 27 | Linear OA(2158, 32806, F2, 21) (dual of [32806, 32648, 22]-code) | [i] | ||
| 28 | Linear OA(2128, 32806, F2, 17) (dual of [32806, 32678, 18]-code) | [i] | ||
| 29 | Linear OA(2260, 16420, F2, 37) (dual of [16420, 16160, 38]-code) | [i] | ||
| 30 | Linear OA(2232, 16420, F2, 33) (dual of [16420, 16188, 34]-code) | [i] | ||
| 31 | Linear OA(2204, 16420, F2, 29) (dual of [16420, 16216, 30]-code) | [i] | ||
| 32 | Linear OA(2176, 16420, F2, 25) (dual of [16420, 16244, 26]-code) | [i] | ||
| 33 | Linear OA(2148, 16420, F2, 21) (dual of [16420, 16272, 22]-code) | [i] | ||
| 34 | Linear OA(2120, 16420, F2, 17) (dual of [16420, 16300, 18]-code) | [i] | ||
| 35 | Linear OA(221, 77, F2, 7) (dual of [77, 56, 8]-code) | [i] | ✔ | Construction XX with Cyclic Codes |
| 36 | Linear OA(2250, 4194355, F2, 23) (dual of [4194355, 4194105, 24]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 37 | Linear OA(2206, 4194355, F2, 19) (dual of [4194355, 4194149, 20]-code) | [i] | ||
| 38 | Linear OA(2239, 2097201, F2, 23) (dual of [2097201, 2096962, 24]-code) | [i] | ||
| 39 | Linear OA(2197, 2097201, F2, 19) (dual of [2097201, 2097004, 20]-code) | [i] | ||
| 40 | Linear OA(2228, 1048623, F2, 23) (dual of [1048623, 1048395, 24]-code) | [i] | ||
| 41 | Linear OA(2188, 1048623, F2, 19) (dual of [1048623, 1048435, 20]-code) | [i] | ||
| 42 | Linear OA(2255, 524333, F2, 27) (dual of [524333, 524078, 28]-code) | [i] | ||
| 43 | Linear OA(2217, 524333, F2, 23) (dual of [524333, 524116, 24]-code) | [i] | ||
| 44 | Linear OA(2179, 524333, F2, 19) (dual of [524333, 524154, 20]-code) | [i] | ||
| 45 | Linear OA(2242, 262187, F2, 27) (dual of [262187, 261945, 28]-code) | [i] | ||
| 46 | Linear OA(2206, 262187, F2, 23) (dual of [262187, 261981, 24]-code) | [i] | ||
| 47 | Linear OA(2170, 262187, F2, 19) (dual of [262187, 262017, 20]-code) | [i] | ||
| 48 | Linear OA(2229, 131113, F2, 27) (dual of [131113, 130884, 28]-code) | [i] | ||
| 49 | Linear OA(2195, 131113, F2, 23) (dual of [131113, 130918, 24]-code) | [i] | ||
| 50 | Linear OA(2161, 131113, F2, 19) (dual of [131113, 130952, 20]-code) | [i] | ||
| 51 | Linear OA(2248, 65575, F2, 31) (dual of [65575, 65327, 32]-code) | [i] | ||
| 52 | Linear OA(2216, 65575, F2, 27) (dual of [65575, 65359, 28]-code) | [i] | ||
| 53 | Linear OA(2184, 65575, F2, 23) (dual of [65575, 65391, 24]-code) | [i] | ||
| 54 | Linear OA(2152, 65575, F2, 19) (dual of [65575, 65423, 20]-code) | [i] | ||
| 55 | Linear OA(2233, 32805, F2, 31) (dual of [32805, 32572, 32]-code) | [i] | ||
| 56 | Linear OA(2203, 32805, F2, 27) (dual of [32805, 32602, 28]-code) | [i] | ||
| 57 | Linear OA(2173, 32805, F2, 23) (dual of [32805, 32632, 24]-code) | [i] | ||
| 58 | Linear OA(2143, 32805, F2, 19) (dual of [32805, 32662, 20]-code) | [i] | ||
| 59 | Linear OA(2246, 16419, F2, 35) (dual of [16419, 16173, 36]-code) | [i] | ||
| 60 | Linear OA(2218, 16419, F2, 31) (dual of [16419, 16201, 32]-code) | [i] | ||
| 61 | Linear OA(2190, 16419, F2, 27) (dual of [16419, 16229, 28]-code) | [i] | ||
| 62 | Linear OA(2162, 16419, F2, 23) (dual of [16419, 16257, 24]-code) | [i] | ||
| 63 | Linear OA(2134, 16419, F2, 19) (dual of [16419, 16285, 20]-code) | [i] | ||