MinT - Information on Result #1535519

Information on Result #1535519

Linear OOA(4¹⁰², 486584, F₄, 3, 14) (dual of [(486584, 3), 1459650, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁰², 486584, F₄, 2, 14) (dual of [(486584, 2), 973066, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁰², 524293, F₄, 2, 14) (dual of [(524293, 2), 1048484, 15]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4¹⁰¹, 524293, F₄, 2, 14) (dual of [(524293, 2), 1048485, 15]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁰¹, 1048586, F₄, 14) (dual of [1048586, 1048485, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
      1. linear OA(4¹⁰¹, 1048576, F₄, 14) (dual of [1048576, 1048475, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      2. linear OA(4⁹¹, 1048576, F₄, 13) (dual of [1048576, 1048485, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(4⁰, 10, F₄, 0) (dual of [10, 10, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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(4¹⁰², 162194, F₄, 21, 14) (dual of [(162194, 21), 3405972, 15]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row