MinT - Information on Result #1535669

Information on Result #1535669

Linear OOA(4¹⁰⁶, 31972, F₄, 3, 18) (dual of [(31972, 3), 95810, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁰⁶, 31972, F₄, 2, 18) (dual of [(31972, 2), 63838, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁰⁶, 32772, F₄, 2, 18) (dual of [(32772, 2), 65438, 19]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4¹⁰⁵, 32772, F₄, 2, 18) (dual of [(32772, 2), 65439, 19]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁰⁵, 65544, F₄, 18) (dual of [65544, 65439, 19]-code), using
    - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
      1. linear OA(4¹⁰⁵, 65536, F₄, 18) (dual of [65536, 65431, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      2. linear OA(4⁹⁷, 65536, F₄, 17) (dual of [65536, 65439, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      3. linear OA(4⁰, 8, F₄, 0) (dual of [8, 8, 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(4¹⁰⁶, 10657, F₄, 21, 18) (dual of [(10657, 21), 223691, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row