MinT - Information on Result #1641244

Information on Result #1641244

Linear OOA(3⁶⁹, 62313, F₃, 5, 10) (dual of [(62313, 5), 311496, 11]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁶⁹, 62313, F₃, 2, 10) (dual of [(62313, 2), 124557, 11]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3⁶⁹, 88580, F₃, 2, 10) (dual of [(88580, 2), 177091, 11]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3⁶⁸, 88580, F₃, 2, 10) (dual of [(88580, 2), 177092, 11]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3⁶⁸, 177160, F₃, 10) (dual of [177160, 177092, 11]-code), using
    - constructionÂ X4 applied to C_e(9) âŠ‚ C_e(7) [i] based on
      1. linear OA(3⁶⁷, 177147, F₃, 10) (dual of [177147, 177080, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      2. linear OA(3⁵⁶, 177147, F₃, 8) (dual of [177147, 177091, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      3. linear OA(3¹², 13, F₃, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,3)), using
        dual of repetition code with length 13 [i]
      4. linear OA(3¹, 13, F₃, 1) (dual of [13, 12, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(3⁶⁹, 62312, F₃, 15, 10) (dual of [(62312, 15), 934611, 11]-NRT-code)	[i]		OOA Stacking with Additional Row