Computing separability elements for the sentence-ambient algebra of split ideal codes. (November 2017)

• Record Type: Journal Article
• Authors: Gómez-Torrecillas, José; Lobillo, F.J.; Navarro, Gabriel
• Is Part Of: Journal of symbolic computation. Volume 83(2017)
• Page Start: 211
• Page End: 227
• Publication Date: 2017-11
• Subjects: 16S36 -- 16Z05 -- 68P30; Split ideal code -- Separable automorphism -- Separable ring extension; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.11.012
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Cyclic structures on convolutional codes are modeled using an Ore extension A [ z ; σ ] of a finite semisimple algebra A over a finite field F . In this context, the separability of the ring extension F [ z ] ⊂ A [ z ; σ ] implies that every ideal code is a split ideal code. We characterize this separability by means of σ being a separable automorphism of the F -algebra A . We design an algorithm that decides if such a given automorphism σ is separable. In addition, it also computes a separability element of F [ z ] ⊂ A [ z ; σ ], which is important because it can be used to find an idempotent generator of each ideal code with sentence-ambient A [ z ; σ ] .