MinT - Information on Result #1420366

Information on Result #1420366

Linear OOA(4⁶¹, 1046403, F₄, 2, 8) (dual of [(1046403, 2), 2092745, 9]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4⁶¹, 1046403, F₄, 8) (dual of [1046403, 1046342, 9]-code), using

discarding factors / shortening the dual code based on linear OA(4⁶¹, 1048587, F₄, 8) (dual of [1048587, 1048526, 9]-code), using
- 1 times truncation [i] based on linear OA(4⁶², 1048588, F₄, 9) (dual of [1048588, 1048526, 10]-code), using
  - constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
    1. linear OA(4⁶¹, 1048576, F₄, 9) (dual of [1048576, 1048515, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    2. linear OA(4⁵¹, 1048576, F₄, 7) (dual of [1048576, 1048525, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    3. linear OA(4¹¹, 12, F₄, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,4)), using
      - dual of repetition code with length 12 [i]
    4. linear OA(4¹, 12, F₄, 1) (dual of [12, 11, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(4⁶¹, 523201, F₄, 3, 8) (dual of [(523201, 3), 1569542, 9]-NRT-code)	[i]		OOA Folding
2	Linear OOA(4⁶¹, 523201, F₄, 10, 8) (dual of [(523201, 10), 5231949, 9]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row