N-ary Codes Research Articles

Task interleaving and orientation estimation for high-precision oriented object detection in aerial images

Oriented object detection in aerial images has received extensive attention due to its wide range of application scenarios. Although great success has been achieved, current methods still suffer from inferior high-precision detection performance. Firstly, the classification scores cannot truly represent the localization accuracy of the predictions. Secondly, the orientation prediction in these detectors is not accurate enough for high-precision object detection. In this paper, we propose a Task Interleaving and Orientation Estimation Detector (TIOE-Det) for high-quality oriented object detection in aerial images. Specifically, a posterior hierarchical alignment (PHA) label is proposed to optimize the detection pipeline. TIOE-Det adopts PHA label to integrate fine-grained posterior localization guidance into classification task to address the misalignment between classification and localization subtasks. Then, a balanced alignment loss is developed to solve the imbalance localization loss contribution in PHA prediction. Moreover, we propose a progressive orientation estimation (POE) strategy to approximate the orientation of objects with n-ary codes. On this basis, an angular deviation weighting strategy is proposed to achieve accurate evaluation of angle deviation in POE strategy. TIOE-Det achieves significant gains on high-precision detection performance. Extensive experiments on multiple datasets prove the superiority of our approach. Codes are available at https://github.com/ming71/TIOE.

Maximal<tex>q</tex>-nary linear codes with large minimum distance (Corresp.)

This correspondence presents a complete solution to the problem of constructing maximal q -nary codes, for any word length n and minimum distance d in the region qd \geq (q - 1)n . Several interesting results regarding the interdependence of these codes are developed, which reveal the unique structure of the code spaces of the region qd \geq (q - 1)n . Some new maximal codes are obtained for the region qd .

Semilinear codes and some combinatorial applications of them

Perfect q -nary codes containing every scalar multiple of each code-vector are constructed and used to generate various combinatorial designs. The obtained 4th order tactical configuration of 13 elements is not closed and is for q = 3 a counterexample similar to that given by Assmus and Mattson (1967) in the binary case.

A note on<tex>p</tex>-nary adjacent-error-correcting codes

Binary group codes described by Abramson permit the correction of all single errors and all double errors in adjacent digits, with the use of significantly fewer check digits than codes capable of correcting all double-bit errors. This note considers the generalization of Abramson's codes to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> -nary case, where a symbol alphabet consisting of the digits <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0, 1, \cdots , p - 1</tex> is used for transmission, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> being a prime number. Examples of such <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> -nary codes are given, as well as necessary conditions for their existence. These codes bear the same relation to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> -nary Golay codes as Abramson's codes do to the familiar Hamming codes. Some as yet unanswered questions are raised, and suggestions for further possible generalizations are given.