{"product_id":"counting-polynomial-matrices-over-finite-fields","title":"Counting Polynomial Matrices over Finite Fields","description":"\u003cp\u003eThis book is dealing with three mathematical areas, namely polynomial matrices over finite fields, linear systems and coding theory.\u003c\/p\u003e\u003cp\u003ePrimeness properties of polynomial matrices provide criteria for the reachability and observability of interconnected linear systems. Since time-discrete linear systems over finite fields and convolutional codes are basically the same objects, these results could be transferred to criteria for non-catastrophicity of convolutional codes.\u003c\/p\u003e\u003cp\u003eIn particular, formulas for the number of pairwise coprime polynomials and for the number of mutually left coprime polynomial matrices are calculated. This leads to the probability that a parallel connected linear system is reachable and that a parallel connected convolutional code is non-catastrophic. Moreover, other networks of linear systems and convolutional codes are considered.\u003c\/p\u003e","brand":"Würzburg University Press","offers":[{"title":"Default Title","offer_id":52691482345839,"sku":"9783958260641","price":217.87,"currency_code":"BRL","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0921\/9384\/9711\/files\/3958260640.jpg?v=1771539293","url":"https:\/\/internacional.umlivro.com.br\/products\/counting-polynomial-matrices-over-finite-fields","provider":"UmLivro Internacional","version":"1.0","type":"link"}