MinT - Information on Result #1535141

Information on Result #1535141

Linear OOA(4⁹¹, 121640, F₄, 3, 14) (dual of [(121640, 3), 364829, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4⁹¹, 121640, F₄, 2, 14) (dual of [(121640, 2), 243189, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4⁹¹, 131076, F₄, 2, 14) (dual of [(131076, 2), 262061, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4⁹¹, 262152, F₄, 14) (dual of [262152, 262061, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(4⁹¹, 262153, F₄, 14) (dual of [262153, 262062, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
      1. linear OA(4⁹¹, 262144, F₄, 14) (dual of [262144, 262053, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      2. linear OA(4⁸², 262144, F₄, 13) (dual of [262144, 262062, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(4⁰, 9, F₄, 0) (dual of [9, 9, 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(4⁹¹, 40546, F₄, 21, 14) (dual of [(40546, 21), 851375, 15]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row