Information on Result #1300956

Linear OA(4246, 263, F4, 157) (dual of [263, 17, 158]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4227, 243, F4, 157) (dual of [243, 16, 158]-code), using
    • 14 times truncation [i] based on linear OA(4241, 257, F4, 171) (dual of [257, 16, 172]-code), using
      • the expurgated narrow-sense BCH-code C(I) with length 257 | 48−1, defining interval I = [0,85], and minimum distance d ≥ |{−85,−84,…,85}|+1 = 172 (BCH-bound) [i]
  2. linear OA(4227, 244, F4, 138) (dual of [244, 17, 139]-code), using Gilbert–VarÅ¡amov bound and bm = 4227 > Vbs−1(k−1) = 40269 414111 539699 333707 093774 056157 603423 140031 721722 130665 195297 419280 610069 744465 176655 416307 877267 417387 787215 315280 521364 120993 650988 [i]
  3. linear OA(418, 19, F4, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,4)), 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:

ResultThis
result
only		Method
1Linear OA(4246, 263, F4, 156) (dual of [263, 17, 157]-code) [i]Strength Reduction
2Linear OA(4243, 260, F4, 154) (dual of [260, 17, 155]-code) [i]Truncation