MinT - Information on Result #1602824

Information on Result #1602824

Linear OOA(3¹⁰⁴, 65183, F₃, 4, 14) (dual of [(65183, 4), 260628, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁰⁴, 65183, F₃, 2, 14) (dual of [(65183, 2), 130262, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁰⁴, 88586, F₃, 2, 14) (dual of [(88586, 2), 177068, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁰⁴, 177172, F₃, 14) (dual of [177172, 177068, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁰⁴, 177173, F₃, 14) (dual of [177173, 177069, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(10) [i] based on
      1. 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]
      2. linear OA(3⁷⁸, 177147, F₃, 11) (dual of [177147, 177069, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. 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(3¹⁰⁴, 32591, F₃, 20, 14) (dual of [(32591, 20), 651716, 15]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row