Information on Result #613735

Linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16

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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(584, 78124, F5, 15) (dual of [78124, 78040, 16]-code) [i]Truncation
2Linear OA(593, 78134, F5, 16) (dual of [78134, 78041, 17]-code) [i](u, u+v)-Construction
3Linear OA(594, 78136, F5, 16) (dual of [78136, 78042, 17]-code) [i]
4Linear OA(595, 78138, F5, 16) (dual of [78138, 78043, 17]-code) [i]
5Linear OA(596, 78141, F5, 16) (dual of [78141, 78045, 17]-code) [i]
6Linear OA(596, 78137, F5, 16) (dual of [78137, 78041, 17]-code) [i](u, u−v, u+v+w)-Construction
7Linear OA(592, 78132, F5, 17) (dual of [78132, 78040, 18]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
8Linear OA(586, 78133, F5, 16) (dual of [78133, 78047, 17]-code) [i]✔
9Linear OA(5100, 78140, F5, 18) (dual of [78140, 78040, 19]-code) [i]✔
10Linear OA(588, 78142, F5, 16) (dual of [78142, 78054, 17]-code) [i]✔
11Linear OA(5109, 78149, F5, 19) (dual of [78149, 78040, 20]-code) [i]✔
12Linear OA(589, 78150, F5, 16) (dual of [78150, 78061, 17]-code) [i]✔
13Linear OA(5121, 78161, F5, 21) (dual of [78161, 78040, 22]-code) [i]✔
14Linear OA(5117, 78151, F5, 20) (dual of [78151, 78034, 21]-code) [i]✔
15Linear OA(5118, 78158, F5, 20) (dual of [78158, 78040, 21]-code) [i]✔
16Linear OA(593, 78161, F5, 16) (dual of [78161, 78068, 17]-code) [i]✔
17Linear OA(5130, 78170, F5, 22) (dual of [78170, 78040, 23]-code) [i]✔
18Linear OA(595, 78170, F5, 15) (dual of [78170, 78075, 16]-code) [i]✔
19Linear OA(5139, 78179, F5, 23) (dual of [78179, 78040, 24]-code) [i]✔
20Linear OA(5149, 78187, F5, 24) (dual of [78187, 78038, 25]-code) [i]✔
21Linear OA(5150, 78190, F5, 24) (dual of [78190, 78040, 25]-code) [i]✔
22Linear OA(5119, 78155, F5, 21) (dual of [78155, 78036, 22]-code) [i]✔
23Linear OA(5120, 78160, F5, 21) (dual of [78160, 78040, 22]-code) [i]✔
24Linear OA(591, 78155, F5, 16) (dual of [78155, 78064, 17]-code) [i]✔
25Linear OA(592, 78160, F5, 16) (dual of [78160, 78068, 17]-code) [i]✔
26Linear OA(5129, 78169, F5, 22) (dual of [78169, 78040, 23]-code) [i]✔
27Linear OA(596, 78170, F5, 16) (dual of [78170, 78074, 17]-code) [i]✔
28Linear OA(594, 78169, F5, 15) (dual of [78169, 78075, 16]-code) [i]✔
29Linear OA(5149, 78189, F5, 24) (dual of [78189, 78040, 25]-code) [i]✔
30Linear OA(5147, 78187, F5, 24) (dual of [78187, 78040, 25]-code) [i]✔
31Linear OA(5120, 78155, F5, 21) (dual of [78155, 78035, 22]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
32Linear OA(5118, 78152, F5, 21) (dual of [78152, 78034, 22]-code) [i]✔
33Linear OA(5108, 78142, F5, 19) (dual of [78142, 78034, 20]-code) [i]✔
34Linear OA(5113, 78156, F5, 19) (dual of [78156, 78043, 20]-code) [i]✔
35Linear OA(5112, 78154, F5, 19) (dual of [78154, 78042, 20]-code) [i]✔
36Linear OA(5111, 78152, F5, 19) (dual of [78152, 78041, 20]-code) [i]✔
37Linear OA(5102, 78143, F5, 18) (dual of [78143, 78041, 19]-code) [i]✔
38Linear OA(594, 78135, F5, 17) (dual of [78135, 78041, 18]-code) [i]✔
39Linear OA(587, 78135, F5, 16) (dual of [78135, 78048, 17]-code) [i]✔
40Linear OA(592, 78155, F5, 16) (dual of [78155, 78063, 17]-code) [i]✔
41Linear OA(590, 78152, F5, 16) (dual of [78152, 78062, 17]-code) [i]✔
42Linear OA(5107, 78148, F5, 18) (dual of [78148, 78041, 19]-code) [i]✔Construction X4 with Extended Narrow-Sense BCH Codes
43Linear OOA(585, 39062, F5, 2, 16) (dual of [(39062, 2), 78039, 17]-NRT-code) [i]OOA Folding
44Linear OOA(585, 26041, F5, 3, 16) (dual of [(26041, 3), 78038, 17]-NRT-code) [i]
45Linear OOA(585, 9765, F5, 16, 16) (dual of [(9765, 16), 156155, 17]-NRT-code) [i]OA Folding and Stacking