MinT - Information on Result #1014743

Information on Result #1014743

Linear OOA(8¹⁷¹, 5593776, F₈, 3, 18) (dual of [(5593776, 3), 16781157, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8³³, 1374, F₈, 3, 9) (dual of [(1374, 3), 4089, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8⁴, 9, F₈, 3, 4) (dual of [(9, 3), 23, 5]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;23,8) [i]
  2. linear OOA(8²⁹, 1365, F₈, 3, 9) (dual of [(1365, 3), 4066, 10]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(8²⁹, 4095, F₈, 9) (dual of [4095, 4066, 10]-code), using
      - discarding factors / shortening the dual code based on linear OA(8²⁹, 4096, F₈, 9) (dual of [4096, 4067, 10]-code), using
        an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 8⁴âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
linear OOA(8¹³⁸, 5592402, F₈, 3, 18) (dual of [(5592402, 3), 16777068, 19]-NRT-code), using
- trace code [i] based on linear OOA(64⁶⁹, 2796201, F₆₄, 3, 18) (dual of [(2796201, 3), 8388534, 19]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(64⁶⁹, large, F₆₄, 18) (dual of [large, large−69, 19]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹⁷¹, 1864591, F₈, 21, 18) (dual of [(1864591, 21), 39156240, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row