MinT - Information on Result #2232850

Information on Result #2232850

Linear OA(3²⁴², 258, F₃, 141) (dual of [258, 16, 142]-code), using 5 times truncation based on linear OA(3²⁴⁷, 263, F₃, 146) (dual of [263, 16, 147]-code), using

constructionÂ X applied to C_e(151) âŠ‚ C_e(133) [i] based on
1. linear OA(3²³², 243, F₃, 152) (dual of [243, 11, 153]-code), using an extension C_e(151) of the primitive narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [1,151], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 152 [i]
2. linear OA(3²²⁷, 243, F₃, 134) (dual of [243, 16, 135]-code), using an extension C_e(133) of the primitive narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [1,133], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 134 [i]
3. linear OA(3¹⁵, 20, F₃, 11) (dual of [20, 5, 12]-code), using
  - residual code [i] based on linear OA(3⁵⁰, 56, F₃, 35) (dual of [56, 6, 36]-code), using
    - dual code (with bound on d by constructionÂ Y1) [i] based on
      1. linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
        the Hill cap [i]
      2. nonexistence of linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), because
        20 is the largest size of a cap in PG(4,Â 3) [i]

Mode: Constructive and 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(3²⁴², 129, F₃, 2, 141) (dual of [(129, 2), 16, 142]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3²⁴², 86, F₃, 3, 141) (dual of [(86, 3), 16, 142]-NRT-code)	[i]		OOA Folding