MinT - Information on Result #1535520

Information on Result #1535520

Linear OOA(4¹⁰², 1582898, F₄, 3, 13) (dual of [(1582898, 3), 4748592, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁰², 1582898, F₄, 2, 13) (dual of [(1582898, 2), 3165694, 14]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁰², 2097158, F₄, 2, 13) (dual of [(2097158, 2), 4194214, 14]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4¹⁰¹, 2097158, F₄, 2, 13) (dual of [(2097158, 2), 4194215, 14]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁰¹, 4194316, F₄, 13) (dual of [4194316, 4194215, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(10) [i] based on
      1. linear OA(4¹⁰⁰, 4194304, F₄, 13) (dual of [4194304, 4194204, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(4⁸⁹, 4194304, F₄, 11) (dual of [4194304, 4194215, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. 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(4¹⁰², 791448, F₄, 15, 13) (dual of [(791448, 15), 11871618, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row