MinT - Information on Result #1607297

Information on Result #1607297

Linear OOA(3¹⁸³, 53322, F₃, 4, 25) (dual of [(53322, 4), 213105, 26]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁸³, 53322, F₃, 3, 25) (dual of [(53322, 3), 159783, 26]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁸³, 59058, F₃, 3, 25) (dual of [(59058, 3), 176991, 26]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁸², 59058, F₃, 3, 25) (dual of [(59058, 3), 176992, 26]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹⁸², 177174, F₃, 25) (dual of [177174, 176992, 26]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(3¹⁸¹, 177173, F₃, 25) (dual of [177173, 176992, 26]-code), using
      - constructionÂ X applied to C_e(24) âŠ‚ C_e(21) [i] based on
        linear OA(3¹⁷⁷, 177147, F₃, 25) (dual of [177147, 176970, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
        linear OA(3¹⁵⁵, 177147, F₃, 22) (dual of [177147, 176992, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        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(3¹⁸³, 17773, F₃, 28, 25) (dual of [(17773, 28), 497461, 26]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row