MinT - Information on Result #1324142

Information on Result #1324142

Linear OA(4²²⁸, 1048654, F₄, 28) (dual of [1048654, 1048426, 29]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4²²⁵, 1048650, F₄, 28) (dual of [1048650, 1048425, 29]-code), using
- 1 times truncation [i] based on linear OA(4²²⁶, 1048651, F₄, 29) (dual of [1048651, 1048425, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(20) [i] based on
    1. linear OA(4²¹¹, 1048576, F₄, 29) (dual of [1048576, 1048365, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    2. linear OA(4¹⁵¹, 1048576, F₄, 21) (dual of [1048576, 1048425, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    3. linear OA(4¹⁵, 75, F₄, 7) (dual of [75, 60, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁵, 85, F₄, 7) (dual of [85, 70, 8]-code), using
        a code from Grasslâ€™s database [i]
linear OA(4²²⁵, 1048651, F₄, 25) (dual of [1048651, 1048426, 26]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4²²⁵Â > V_b^sâˆ’1(kâˆ’1)Â = 1 423072 150412 636387 036637 764552 218908 154717 981249 998054 144591 515161 012680 168427 035153 324128 086486 812233 457411 000364 551483 729118 645156 [i]
linear OA(4², 3, F₄, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,4)), using
- dual of repetition code with length 3 [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(4²²⁸, 524327, F₄, 2, 28) (dual of [(524327, 2), 1048426, 29]-NRT-code)	[i]		OOA Folding