Computer classification of linear codes

We present algorithms for classification of linear codes over finite fields, based on canonical augmentation and on lattice point enumeration. We apply these algorithms to obtain classification results over fields with 2, 3 and 4 elements. We validate a correct implementation of the algorithms with known classification results from the literature, which we partially extend to larger ranges of parameters.Comment: 18 pages, 9 tables; this paper is a merge and extension of arXiv:1907.10363 and arXiv:1912.0935

LinCode - computer classification of linear codes

We present an algorithm for the classification of linear codes over finite fields, based on lattice point enumeration. We validate a correct implementation of our algorithm with known classification results from the literature, which we partially extend to larger ranges of parameters.Comment: 12 pages, 5 table

Optimal binary linear codes of dimension at most seven

AbstractWe classify optimal [n,k,d] binary linear codes of dimension ⩽7, with one exception, where by optimal we mean that no [n−1,k,d],[n+1,k+1,d], or [n+1,k,d+1] code exists. In particular, we present (new) classification results for codes with parameters [40,7,18], [43,7,20], [59,7,28], [75,7,36], [79,7,38], [82,7,40], [87,7,42], and [90,7,44]. These classifications are accomplished with the aid of the first author's computer program Extension for extending from residual codes, and the second author's program Split

A generalization of the cylinder conjecture for divisible codes

We extend the original cylinder conjecture on point sets in affine three-dimensional space to the more general framework of divisible linear codes over $\mathbb{F}_q$ and their classification. Through a mix of linear programming, combinatorial techniques and computer enumeration, we investigate the structural properties of these codes. In this way, we can prove a reduction theorem for a generalization of the cylinder conjecture, show some instances where it does not hold and prove its validity for small values of $q$. In particular, we correct a flawed proof for the original cylinder conjecture for $q = 5$ and present the first proof for $q = 7$.Comment: 16 page

Exemplar codes for facial attributes and tattoo recognition

Abstract When implementing real-world computer vision systems, researchers can use mid-level representations as a tool to adjust the trade-off between accuracy and efficiency. Unfortunately, existing mid-level representations that improve accuracy tend to decrease efficiency, or are specifically tailored to work well within one pipeline or vision problem at the exclusion of others. We introduce a novel, efficient mid-level representation that improves classification efficiency without sacrificing accuracy. Our Exemplar Codes are based on linear classifiers and probability normalization from extreme value theory. We apply Exemplar Codes to two problems: facial attribute extraction and tattoo classification. In these settings, our Exemplar Codes are competitive with the state of the art and offer efficiency benefits, making it possible to achieve high accuracy even on commodity hardware with a low computational budget

Semi-Supervised Sparse Coding

Sparse coding approximates the data sample as a sparse linear combination of some basic codewords and uses the sparse codes as new presentations. In this paper, we investigate learning discriminative sparse codes by sparse coding in a semi-supervised manner, where only a few training samples are labeled. By using the manifold structure spanned by the data set of both labeled and unlabeled samples and the constraints provided by the labels of the labeled samples, we learn the variable class labels for all the samples. Furthermore, to improve the discriminative ability of the learned sparse codes, we assume that the class labels could be predicted from the sparse codes directly using a linear classifier. By solving the codebook, sparse codes, class labels and classifier parameters simultaneously in a unified objective function, we develop a semi-supervised sparse coding algorithm. Experiments on two real-world pattern recognition problems demonstrate the advantage of the proposed methods over supervised sparse coding methods on partially labeled data sets