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High-throughput blockchains require efficient transaction broadcast mechanisms that can deliver transactions to most network nodes with low bandwidth overhead and latency. Existing schemes coordinate transmissions across peers to avoid sending redundant data, but they either incur a high latency or are not robust against adversarial network nodes. We present Strokkur, a new transaction broadcasting mechanism that provides both low bandwidth overhead and low latency. The core idea behind Strokkur is to avoid explicit coordination through randomized transaction coding. Rather than forward individual transactions. Strokkur nodes send out codewords -- XOR sums of multiple transactions selected at random. Since almost every codeword is useful for the receiver to decode new transactions, Strokkur nodes do not require coordination, for example, to determine which transactions the receiver is missing. Strokkur's coding strategy builds on LT codes, a popular class of rateless erasure codes, and extends them to support multiple uncoordinated senders with partially-overlapping continual streams of transaction data. Strokkur introduces mechanisms to cope with adversarial senders that may send corrupt codewords, and a simple rate control algorithm that enables each node to independently determine an appropriate sending rate of codewords for each peer. Our implementation of Strokkur in Golang supports 647k transactions per second using only one CPU core. Our evaluation across a 19-node Internet deployment and large-scale simulation show that Strokkur consumes 2--7.6x less bandwidth than the existing scheme in Bitcoin, and 9x lower latency that Shrec when only 4% of nodes are adversarial.