MinT - Information on Result #1542125

Information on Result #1542125

Linear OOA(4²¹⁰, 111749, F₄, 3, 31) (dual of [(111749, 3), 335037, 32]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4²¹⁰, 111749, F₄, 2, 31) (dual of [(111749, 2), 223288, 32]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4²¹⁰, 131082, F₄, 2, 31) (dual of [(131082, 2), 261954, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4²¹⁰, 262164, F₄, 31) (dual of [262164, 261954, 32]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(4²⁰⁹, 262163, F₄, 31) (dual of [262163, 261954, 32]-code), using
    - constructionÂ X applied to C_e(30) âŠ‚ C_e(28) [i] based on
      1. linear OA(4²⁰⁸, 262144, F₄, 31) (dual of [262144, 261936, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      2. linear OA(4¹⁹⁰, 262144, F₄, 29) (dual of [262144, 261954, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      3. linear OA(4¹, 19, F₄, 1) (dual of [19, 18, 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(4²¹⁰, 22349, F₄, 33, 31) (dual of [(22349, 33), 737307, 32]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row