MinT - Information on Result #1522069

Information on Result #1522069

Linear OOA(3¹⁰⁵, 72030, F₃, 3, 14) (dual of [(72030, 3), 215985, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁰⁵, 72030, F₃, 2, 14) (dual of [(72030, 2), 143955, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁰⁵, 88587, F₃, 2, 14) (dual of [(88587, 2), 177069, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁰⁵, 177174, F₃, 14) (dual of [177174, 177069, 15]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3¹⁰⁴, 177173, F₃, 14) (dual of [177173, 177069, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(10) [i] based on
      1. linear OA(3¹⁰⁰, 177147, F₃, 14) (dual of [177147, 177047, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      2. linear OA(3⁷⁸, 177147, F₃, 11) (dual of [177147, 177069, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(3⁴, 26, F₃, 2) (dual of [26, 22, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [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(3¹⁰⁵, 36015, F₃, 5, 14) (dual of [(36015, 5), 179970, 15]-NRT-code)	[i]		OOA Folding