MinT - Information on Result #1646538

Information on Result #1646538

Linear OOA(3¹⁷⁹, 185675, F₃, 5, 21) (dual of [(185675, 5), 928196, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁷⁹, 185675, F₃, 2, 21) (dual of [(185675, 2), 371171, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁷⁹, 265749, F₃, 2, 21) (dual of [(265749, 2), 531319, 22]-NRT-code), using
- 1 step truncation [i] based on linear OOA(3¹⁸⁰, 265750, F₃, 2, 22) (dual of [(265750, 2), 531320, 23]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁸⁰, 531500, F₃, 22) (dual of [531500, 531320, 23]-code), using
    - constructionÂ X applied to C_e(21) âŠ‚ C_e(15) [i] based on
      1. linear OA(3¹⁶⁹, 531441, F₃, 22) (dual of [531441, 531272, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      2. linear OA(3¹²¹, 531441, F₃, 16) (dual of [531441, 531320, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      3. linear OA(3¹¹, 59, F₃, 5) (dual of [59, 48, 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(3¹⁷⁹, 92837, F₃, 25, 21) (dual of [(92837, 25), 2320746, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row