MinT - Information on Result #1641320

Information on Result #1641320

Linear OOA(3⁷², 28143, F₃, 5, 11) (dual of [(28143, 5), 140643, 12]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁷², 28143, F₃, 2, 11) (dual of [(28143, 2), 56214, 12]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3⁷², 29530, F₃, 2, 11) (dual of [(29530, 2), 58988, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁷², 59060, F₃, 11) (dual of [59060, 58988, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁷², 59061, F₃, 11) (dual of [59061, 58989, 12]-code), using
    - constructionÂ X4 applied to C([0,10]) âŠ‚ C([1,9]) [i] based on
      1. linear OA(3⁷¹, 59048, F₃, 11) (dual of [59048, 58977, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      2. linear OA(3⁶⁰, 59048, F₃, 9) (dual of [59048, 58988, 10]-code), using the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      3. linear OA(3¹², 13, F₃, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,3)), using
        dual of repetition code with length 13 [i]
      4. linear OA(3¹, 13, F₃, 1) (dual of [13, 12, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 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(3⁷², 28142, F₃, 15, 11) (dual of [(28142, 15), 422058, 12]-NRT-code)	[i]		OOA Stacking with Additional Row