In a linear wireless sensor network (LWSN), sensor nodes are deployed in a linear fashion to monitor and gather data along a linear path or route. Generally, the base station collects the data from the contiguously placed nodes in the same order. When the sensors are deployed closely and with a gradual variation of sensor data along the route, a high degree of correlation exists among the sensed data. The sensed data sequence can be compressed with very low loss in such a situation. In this paper, a joint compression and encryption method for LWSN data is presented. The method is based on the dimension reduction property of an autoencoder at the bottleneck section. The Encoder part of the trained Autoencoder, housed at the Base Station (BS), reduces the number of data samples at the encoded output. Hence, the data gets compressed at the output of the Encoder. The output of the Encoder is encrypted using an asymmetric encryption that provides immunity to the Chosen Plaintext Attack. Thus, both data compression and encryption are achieved together at the BS. Therefore, the procedure at the BS is denoted as joint compression and encryption. The encrypted data is sent to the Cloud Server for secured storage and further distribution to the End User, where it is decrypted and subsequently decompressed by the Decoder part of the trained Autoencoder. The decompressed data sequence is very nearly equal to the original data sequence. The proposed lossy compression has a mean square reconstruction error of less than 0.5 for compression ratios in the range of 5 to 10. The compression time taken is short even though the Autoencoder training process, which occurs once in a while, takes a relatively long time.