MinT - Information on Result #2478571

Information on Result #2478571

Linear OOA(2²³¹, 4195332, F₂, 2, 16) (dual of [(4195332, 2), 8390433, 17]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2²²⁹, 4195331, F₂, 2, 16) (dual of [(4195331, 2), 8390433, 17]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁴⁵, 1030, F₂, 2, 8) (dual of [(1030, 2), 2015, 9]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2⁴⁵, 2060, F₂, 8) (dual of [2060, 2015, 9]-code), using
    - 1 times truncation [i] based on linear OA(2⁴⁶, 2061, F₂, 9) (dual of [2061, 2015, 10]-code), using
      - constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
        linear OA(2⁴⁵, 2048, F₂, 9) (dual of [2048, 2003, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(2³⁴, 2048, F₂, 7) (dual of [2048, 2014, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(2¹², 13, F₂, 11) (dual of [13, 1, 12]-code), using
        strength reduction [i] based on linear OA(2¹², 13, F₂, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,2)), using
        dual of repetition code with length 13 [i]
        linear OA(2¹, 13, F₂, 1) (dual of [13, 12, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OOA(2¹⁸⁴, 4194301, F₂, 2, 16) (dual of [(4194301, 2), 8388418, 17]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹⁸⁴, 8388602, F₂, 16) (dual of [8388602, 8388418, 17]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹⁸⁴, large, F₂, 16) (dual of [large, large−184, 17]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m 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(2²³¹, 2097666, F₂, 4, 16) (dual of [(2097666, 4), 8390433, 17]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²³¹, 1048833, F₂, 8, 16) (dual of [(1048833, 8), 8390433, 17]-NRT-code)	[i]		OOA Folding