MinT - Information on Result #1521166

Information on Result #1521166

Linear OOA(3⁷⁸, 255889, F₃, 3, 10) (dual of [(255889, 3), 767589, 11]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁷⁸, 255889, F₃, 2, 10) (dual of [(255889, 2), 511700, 11]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3⁷⁸, 265735, F₃, 2, 10) (dual of [(265735, 2), 531392, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁷⁸, 531470, F₃, 10) (dual of [531470, 531392, 11]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3⁷⁷, 531469, F₃, 10) (dual of [531469, 531392, 11]-code), using
    - constructionÂ X applied to C_e(9) âŠ‚ C_e(6) [i] based on
      1. linear OA(3⁷³, 531441, F₃, 10) (dual of [531441, 531368, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      2. linear OA(3⁴⁹, 531441, F₃, 7) (dual of [531441, 531392, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(3⁴, 28, F₃, 2) (dual of [28, 24, 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(3⁷⁸, 127944, F₃, 5, 10) (dual of [(127944, 5), 639642, 11]-NRT-code)	[i]		OOA Folding