Some conjectures on codes
نویسنده
چکیده
Variable-length codes are the bases of the free submonoids of a free monoid. There are some important longstanding open questions about the structure of finite maximal codes. In this paper we discuss this conjectures and their relations with factorizations of cyclic groups.
منابع مشابه
Proof of Conjectures on the True Dimension of Some Binary Goppa Codes
There is a classical lower bound on the dimension of a binary Goppa code. We survey results on some specific codes whose dimension exceeds this bound, and prove two conjectures on the true dimension of two classes of such codes.
متن کاملSome new families of definite polynomials and the composition conjectures
The planar polynomial vector fields with a center at the origin can be written as an scalar differential equation, for example Abel equation. If the coefficients of an Abel equation satisfy the composition condition, then the Abel equation has a center at the origin. Also the composition condition is sufficient for vanishing the first order moments of the coefficients. The composition conjectur...
متن کاملDesigns and Codes: An update
Since the publication in 1992 of “Designs and their Codes” significant progress has been made in the general area of codes coming from designs. This article reviews this progress and presents some of the results — including confirmation of certain conjectures made and answers to some of the questions raised in the book.
متن کاملProofs of two conjectures on the dimensions of binary codes
Let L and L0 be the binary codes generated by the column F2null space of the incidence matrix of the external points and passant lines and that of the incidence matrix of the internal points and secant lines with respect to a conic in PG(2, q), respectively. We confirm the conjectures on the dimensions of L and L0 using methods from both finite geometry and modular representation theory.
متن کاملConnections between labellings of trees
There are many long-standing conjectures related with some labellings of trees. It is important to connect labellings that are related with conjectures. We find some connections between known labellings of simple graphs.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1611.04580 شماره
صفحات -
تاریخ انتشار 2016