MinT - Information on Result #1546263

Information on Result #1546263

Linear OOA(4²⁵⁴, 458088, F₄, 3, 33) (dual of [(458088, 3), 1374010, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4²⁵⁴, 458088, F₄, 2, 33) (dual of [(458088, 2), 915922, 34]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4²⁵⁴, 524319, F₄, 2, 33) (dual of [(524319, 2), 1048384, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4²⁵⁴, 1048638, F₄, 33) (dual of [1048638, 1048384, 34]-code), using
  - discarding factors / shortening the dual code based on linear OA(4²⁵⁴, 1048639, F₄, 33) (dual of [1048639, 1048385, 34]-code), using
    - constructionÂ X applied to C_e(32) âŠ‚ C_e(25) [i] based on
      1. linear OA(4²⁴¹, 1048576, F₄, 33) (dual of [1048576, 1048335, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
      2. linear OA(4¹⁹¹, 1048576, F₄, 26) (dual of [1048576, 1048385, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      3. linear OA(4¹³, 63, F₄, 6) (dual of [63, 50, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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(4²⁵⁴, 76347, F₄, 39, 33) (dual of [(76347, 39), 2977279, 34]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row