Applicable Algebra in Engineering, Communication and Computing ( IF 0.7 ) Pub Date : 2021-11-20 , DOI: 10.1007/s00200-021-00534-3 Hai Q. Dinh 1 , Abhay Kumar Singh 2 , Madhu Kant Thakur 2
Let \({\mathfrak {R}}={\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}\) with \(u^2=0\), where m, s are positive integers and p is an odd prime. For any invertible element \(\varLambda\) of \({\mathfrak {R}}\), the symbol-pair distances of all \(\varLambda\)-constacyclic codes of length \(2p^s\) over \({\mathfrak {R}}\) are completely obtained. We identify all symbol-pair Maximum Distance Separable (MDS) constacyclic codes of length \(2p^s\) over \({\mathfrak {R}}\). As examples, many new symbol-pair codes, as well as symbol-pair MDS codes are constructed.
中文翻译:
在 $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p 上长度为 $$2p^s$$ 2 ps 的重复根恒循环码的符号对距离^m}$$ F pm + u F pm 和 MDS 符号对代码
让\({\mathfrak {R}}={\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}\)与\(u^2=0\ ),其中m、 s是正整数,p是奇素数。对于\({\mathfrak {R}}\) 的任何可逆元素\(\varLambda\),所有\(\varLambda\) -长度为\(2p^s\) 的恒环码的符号对距离在\ ({\mathfrak {R}}\)完全获得。我们在\({\mathfrak {R}}\) 上识别所有长度为\(2p^s\) 的符号对最大距离可分离 (MDS) 恒环码. 例如,构建了许多新的符号对代码以及符号对 MDS 代码。