By Jaques Calmet
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Additional info for Algebraic Algorithms and Error-Correcting Codes: 3rd International Conference, AAECC-3 Grenoble, France, July 15–19, 1985 Proceedings
I f not (diagonal p a r t i t i o n ) , it corresponds t o two i n d e p e n d e n t c o d i n g schemes. (no p r a c t i c a l a p p l i c a t i o n ) . XXXXXXXXX ! XXXXXXXXX I XXXXXXXXX~ In t h a t case, t h e e i g e n v e c t o r i s n o t u n i q u e . IXXXX IXXXX 3) The t o t a l o f t h e e l e m e n t s o f any row i s i . 4) For a M-ary coded s i g n a l t h e r e i s a maximum o f M e l e m e n t s per row ( l e s s t h a n M i s p o s s i b l e i f t h e r e i s more t h a n 1 branch from one state to another).
For c o n v e n i e n c y , t h e new s t a t e s a r e r e l a b e l l e d using l o w e r case l e t t e r s . The n e x t s t a t e s i n t h i s t a b l e a r e formed by t a k i n g t h e p r o p e r sequence o f t h r e e s t a t e s o f t h e o r i g i n a l diagram r a n k i n g a t # 2~ 3 & 4. For example : S t a r t i n g f r o m s t a t e f = 035v a s o u r c e b i t 1 leads to state 1 in the original diagram, and t o s t a t e 351 = t i n t a b l e below. States 010 020 031 032 034 035 042 101 102 103 104 201 202 203 204 310 320 342 351 420 510 Source b i t !
0 The f i n a l r e s u l t i s • S States States States States States States S I GN b, r & u merge i n t o new s t a t e j , k , n & p merge i n t o new s t a t e h , i , I & m merge i n t o new s t a t e a, q & v merge i n t o new s t a t e c , g l s & t merge i n t o new s t a t e d,e & f merge i n t o new s t a t e I F I C A N T 1 2 3 4 5 6 : : : : : : 3 (01) 5 (00) 4 (00) 3 (I0) 4 (00) 5 (00) (01) (00) (00) (10) (10) (00) R E F E R E N C E S E l ] ADLER, COPPERSMITH & HASSNER " A l g o r i t h m s f o r IEEE - Vol I T 29 - N 1 - JAN 83 - pp 5 - 2 2  4 5 6 2 6 1 2 1 1 sliding B l o c k Codes" CARRIOLARO & A I .
Algebraic Algorithms and Error-Correcting Codes: 3rd International Conference, AAECC-3 Grenoble, France, July 15–19, 1985 Proceedings by Jaques Calmet