Negacyclic codes of length 2^(s) over the Galois ring GR(2a,m)are linearly ordered under set-theoretic inclusion,i.e.,they are the ideals<(x+1)^(i)>,0≤i≤2^(s)a,of the chain ring GR(2^(a),m)[x]/<x^(2s)+1>...Negacyclic codes of length 2^(s) over the Galois ring GR(2a,m)are linearly ordered under set-theoretic inclusion,i.e.,they are the ideals<(x+1)^(i)>,0≤i≤2^(s)a,of the chain ring GR(2^(a),m)[x]/<x^(2s)+1>.This structure is used to obtain the symbol-pair distances of all such negacyclic codes.Among others,for the special case when the alphabet is the finite field F2m(i.e.,a=1),the symbol-pair distance distribution of constacyclic codes over F2m verifies the Singleton bound for such symbol-pair codes,and provides all maximum distance separable symbol-pair constacyclic codes of length 2^(s) over F_(2m).展开更多
The properties of the generator matrix are given for linear codes over finite commutative chain rings, and the so-called almost-MDS （AMDS） codes are studied.
文摘Negacyclic codes of length 2^(s) over the Galois ring GR(2a,m)are linearly ordered under set-theoretic inclusion,i.e.,they are the ideals<(x+1)^(i)>,0≤i≤2^(s)a,of the chain ring GR(2^(a),m)[x]/<x^(2s)+1>.This structure is used to obtain the symbol-pair distances of all such negacyclic codes.Among others,for the special case when the alphabet is the finite field F2m(i.e.,a=1),the symbol-pair distance distribution of constacyclic codes over F2m verifies the Singleton bound for such symbol-pair codes,and provides all maximum distance separable symbol-pair constacyclic codes of length 2^(s) over F_(2m).
基金Supported by the National Natural Science Foundation of China (No. 60402022)
文摘The properties of the generator matrix are given for linear codes over finite commutative chain rings, and the so-called almost-MDS （AMDS） codes are studied.
