MinT - Information on Result #1521566

Information on Result #1521566

Linear OOA(3⁹¹, 88586, F₃, 3, 12) (dual of [(88586, 3), 265667, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁹¹, 88586, F₃, 2, 12) (dual of [(88586, 2), 177081, 13]-NRT-code), using

OOA 2-folding [i] based on linear OA(3⁹¹, 177172, F₃, 12) (dual of [177172, 177081, 13]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3⁹⁰, 177171, F₃, 12) (dual of [177171, 177081, 13]-code), using
  - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(9) [i] based on
    1. linear OA(3⁸⁹, 177147, F₃, 13) (dual of [177147, 177058, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. 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]
    3. linear OA(3²³, 24, F₃, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,3)), using
      - dual of repetition code with length 24 [i]
    4. linear OA(3¹, 24, F₃, 1) (dual of [24, 23, 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(3⁹², 88586, F₃, 3, 12) (dual of [(88586, 3), 265666, 13]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3⁹¹, 44293, F₃, 5, 12) (dual of [(44293, 5), 221374, 13]-NRT-code)	[i]		OOA Folding