RESEARCH ON THE ERROR-CORRECTING CODES BASED ON THE EVALUATION MAPS OF VECTOR BUNDLES

在信息传输过程中纠正错误的数学技术称为纠错码。在本研究中，我们引入了一种由代数簇上的称为矢丛的几何对象定义的新型纠错码，并研究了它们的基本性质。作为我们研究的结果，我们已经证明了从满足称为弱α-稳定性的条件的向量丛中构造良好的码是可能的。

The mathematical technique of correcting the errors in the process of transmission of information is called the error-correcting codes. In the present research, we introduced a new type of error-correcting codes defined by means of the geometric objects called vector bundles on an algebraic variety and investigated their fundamental properties. As a result of our research, we have shown that it is possible to construct good codes from vector bundles which satisfy a condition called weak α-stability.