MinT - Information on Result #1429885

Information on Result #1429885

Linear OOA(4²¹², 16054, F₄, 2, 38) (dual of [(16054, 2), 31896, 39]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4²¹², 16054, F₄, 38) (dual of [16054, 15842, 39]-code), using

discarding factors / shortening the dual code based on linear OA(4²¹², 16434, F₄, 38) (dual of [16434, 16222, 39]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4²¹⁰, 16432, F₄, 38) (dual of [16432, 16222, 39]-code), using
  - constructionÂ X applied to C_e(37) âŠ‚ C_e(30) [i] based on
    1. linear OA(4¹⁹⁷, 16384, F₄, 38) (dual of [16384, 16187, 39]-code), using an extension C_e(37) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,37], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
    2. linear OA(4¹⁶², 16384, F₄, 31) (dual of [16384, 16222, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    3. linear OA(4¹³, 48, F₄, 6) (dual of [48, 35, 7]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹³, 63, F₄, 6) (dual of [63, 50, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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(4²¹², 8027, F₄, 3, 38) (dual of [(8027, 3), 23869, 39]-NRT-code)	[i]		OOA Folding