MinT - Information on Result #1605653

Information on Result #1605653

Linear OOA(3¹⁵⁹, 1506010, F₃, 4, 17) (dual of [(1506010, 4), 6023881, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁵⁹, 1506010, F₃, 3, 17) (dual of [(1506010, 3), 4517871, 18]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁵⁹, 1594333, F₃, 3, 17) (dual of [(1594333, 3), 4782840, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹⁵⁹, 4782999, F₃, 17) (dual of [4782999, 4782840, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁵⁹, 4783001, F₃, 17) (dual of [4783001, 4782842, 18]-code), using
    - constructionÂ X applied to C_e(16) âŠ‚ C_e(13) [i] based on
      1. linear OA(3¹⁵⁵, 4782969, F₃, 17) (dual of [4782969, 4782814, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      2. linear OA(3¹²⁷, 4782969, F₃, 14) (dual of [4782969, 4782842, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      3. linear OA(3⁴, 32, F₃, 2) (dual of [32, 28, 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(3¹⁵⁹, 753004, F₃, 20, 17) (dual of [(753004, 20), 15059921, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row