MinT - Information on Result #1545234

Information on Result #1545234

Linear OOA(4²⁴⁴, 43910, F₄, 3, 39) (dual of [(43910, 3), 131486, 40]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4²⁴⁴, 43910, F₄, 39) (dual of [43910, 43666, 40]-code), using

discarding factors / shortening the dual code based on linear OA(4²⁴⁴, 65587, F₄, 39) (dual of [65587, 65343, 40]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4²⁴³, 65586, F₄, 39) (dual of [65586, 65343, 40]-code), using
  - constructionÂ X applied to C_e(38) âŠ‚ C_e(32) [i] based on
    1. linear OA(4²³³, 65536, F₄, 39) (dual of [65536, 65303, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
    2. linear OA(4¹⁹³, 65536, F₄, 33) (dual of [65536, 65343, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
    3. linear OA(4¹⁰, 50, F₄, 5) (dual of [50, 40, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁰, 63, F₄, 5) (dual of [63, 53, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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(4²⁴⁴, 6272, F₄, 45, 39) (dual of [(6272, 45), 281996, 40]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row