论文标题
有限字段的任意长度的多维恒定型码
Multi-dimensional Constacyclic Codes of Arbitrary Length over Finite Fields
论文作者
论文摘要
多维循环代码是循环代码的自然概括。在较早的论文中，我们在有限字段上探索了二维Constacyclic代码。遵循相同的技术，我们在这里表征了多维constacyclic代码的代数结构，特别是三维$（α，β，β，γ）$ - 任意长度$ s \ ell k $的constacyclic代码及其在有限fielt $ \ nath $ eldement $ \ n $ n wery wery wery n were n were zer的duals上$ \ mathbb {f} _q $。我们为三维$（α，β，γ）$ - constacyclic代码提供了必要的条件。
Multi-dimensional cyclic code is a natural generalization of cyclic code. In an earlier paper we explored two-dimensional constacyclic codes over finite fields. Following the same technique, here we characterize the algebraic structure of multi-dimensional constacyclic codes, in particular three-dimensional $(α,β,γ)$- constacyclic codes of arbitrary length $s\ell k$ and their duals over a finite field $\mathbb{F}_q$, where $α,β,γ$ are non zero elements of $\mathbb{F}_q$. We give necessary and sufficient conditions for a three-dimensional $(α,β,γ)$- constacyclic code to be self-dual.
