MinT - Information on Result #1540984

Information on Result #1540984

Linear OOA(4¹⁹⁶, 31380, F₄, 3, 33) (dual of [(31380, 3), 93944, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁹⁶, 31380, F₄, 2, 33) (dual of [(31380, 2), 62564, 34]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁹⁶, 32777, F₄, 2, 33) (dual of [(32777, 2), 65358, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁹⁶, 65554, F₄, 33) (dual of [65554, 65358, 34]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁹⁶, 65555, F₄, 33) (dual of [65555, 65359, 34]-code), using
    - constructionÂ X applied to C_e(32) âŠ‚ C_e(29) [i] based on
      1. linear OA(4¹⁹³, 65536, F₄, 33) (dual of [65536, 65343, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
      2. linear OA(4¹⁷⁷, 65536, F₄, 30) (dual of [65536, 65359, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      3. linear OA(4³, 19, F₄, 2) (dual of [19, 16, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(4³, 21, F₄, 2) (dual of [21, 18, 3]-code), using
        Hamming code H(3,4) [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(4¹⁹⁶, 5229, F₄, 39, 33) (dual of [(5229, 39), 203735, 34]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row