MinT - Information on Result #1524699

Information on Result #1524699

Linear OOA(3¹⁵⁶, 75332, F₃, 3, 20) (dual of [(75332, 3), 225840, 21]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁵⁶, 75332, F₃, 2, 20) (dual of [(75332, 2), 150508, 21]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁵⁶, 88601, F₃, 2, 20) (dual of [(88601, 2), 177046, 21]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁵⁵, 88601, F₃, 2, 20) (dual of [(88601, 2), 177047, 21]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁵⁵, 177202, F₃, 20) (dual of [177202, 177047, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(13) [i] based on
      1. linear OA(3¹⁴⁴, 177147, F₃, 20) (dual of [177147, 177003, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. 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]
      3. linear OA(3¹¹, 55, F₃, 5) (dual of [55, 44, 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(3¹⁵⁶, 37666, F₃, 5, 20) (dual of [(37666, 5), 188174, 21]-NRT-code)	[i]		OOA Folding