A method is given for the construction of linear codes with pre-scribed minimum distance and also prescribed minimum distance of the dualcode. This works for codes over arbitrary nite elds. In the case of binary
Linear codeHullGaussian sumNumber fieldThe hull of a linear code over finite fields, the intersection of the code and its dual, has been of interest and extensively studied due to its wide applications. For example, it plays a vital role in determining the complexity of algorithms for checking...
Linear codeSubfield codeWeight distributionExponential sumSphere Packing boundRecently, subfield codes of some optimal linear codes have been studied. In this paper, we further investigate a class of subfield codes and generalize the results of the subfield codes of the conic codes in Ding and Wang...
Recall that the linear code CDλ over R is defined by Eq. (2), where Dλ defined by Eq. (3) is called the defining set and nλ=|Dλ| is the length of CDλ Minimal linear codes with wminwmax<p−1p Minimal linear codes have important applications in cryptography, such as ...
因此得出结论,approximating the nearest codeword problem to within factors smaller than (1-1/p)/(1-1/(\alpha p)) on random codes is as hard as quantumly approximating worst-case lattice problems. 以上给出了理解随机线性码的解码问题的部分解答。 Cryptosystem 在Section 5中本文提出了一个公钥加密...
A linear code C is said to be minimal if every codeword of C is minimal. Constructing minimal linear codes is an interesting research topic due to their applications in coding theory and cryptography. For example, minimal linear codes could be decoded with a minimum distance decoding method [...
that approximating the nearest codeword problem to within factors smaller than (1 − 1/p)/(1 − 1/(αp)) on random codes is as hard as quantumly approximating worst-case lattice problems. This gives a partial answer to the important open question of understanding the hardness of decodin...
In this work, we initiate the study of linear batch codes. These codes, in particular, are of potential use in distributed storage systems. We show that a generator matrix of a binary linear batch code is also a generator matrix of classical binary linear error-correcting code. This ...
‘learning from parity with error’ problem to higher moduli. It can also be viewed as the problem of decoding from a random linear code. This, we believe, gives a strong indication that these problems are hard. Our reduction, however, is quantum. Hence, an efficient solution to the ...
Hash functions are a fundamental component of cryptography, serving to efficiently condense messages into fixed-length digests. As one-way functions, they exhibit high sensitivity to even minor changes in the input, making it exceedingly difficult to derive the original message from its hash value....