MinT - Information on Result #1431693

Information on Result #1431693

Linear OOA(4²²⁷, 191366, F₄, 2, 31) (dual of [(191366, 2), 382505, 32]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4²²⁷, 191366, F₄, 31) (dual of [191366, 191139, 32]-code), using

discarding factors / shortening the dual code based on linear OA(4²²⁷, 262167, F₄, 31) (dual of [262167, 261940, 32]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(4¹⁹, 23, F₄, 15) (dual of [23, 4, 16]-code), using
    - constructionÂ X applied to C₁ âŠ‚ C₂ with C₁ a [17,1,16]-code [i] based on
      1. linear OA(4¹³, 17, F₄, 11) (dual of [17, 4, 12]-code), using projective code from ovoid in PG(3,Â 4) [i]
      2. linear OA(4³, 6, F₄, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), using
        hyperoval in PG(2,Â 4) [i]
        the Hexacode [i]
  2. linear OA(4²⁰⁸, 262144, F₄, 31) (dual of [262144, 261936, 32]-code), using
    - an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]

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 OOA(4²²⁷, 95683, F₄, 3, 31) (dual of [(95683, 3), 286822, 32]-NRT-code)	[i]		OOA Folding