MinT - Information on Result #1648381

Information on Result #1648381

Linear OOA(3²⁰³, 25725, F₃, 5, 29) (dual of [(25725, 5), 128422, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁰³, 25725, F₃, 2, 29) (dual of [(25725, 2), 51247, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁰³, 29550, F₃, 2, 29) (dual of [(29550, 2), 58897, 30]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3²⁰², 29550, F₃, 2, 29) (dual of [(29550, 2), 58898, 30]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3²⁰², 59100, F₃, 29) (dual of [59100, 58898, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(22) [i] based on
      1. linear OA(3¹⁹¹, 59049, F₃, 29) (dual of [59049, 58858, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(3¹⁵¹, 59049, F₃, 23) (dual of [59049, 58898, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      3. linear OA(3¹¹, 51, F₃, 5) (dual of [51, 40, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹¹, 85, F₃, 5) (dual of [85, 74, 6]-code), using
        codes constructed by inverting constructionÂ Y₁ [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(3²⁰³, 8574, F₃, 35, 29) (dual of [(8574, 35), 299887, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row