Some new symmetric Hadamard matrices

Introduction: It is conjectured that the symmetric Hadamard matrices of order 4v exist for all odd integers v>0. In recent years, their existence has been proven many new orders by using a special method known as propus construction. This construction uses difference families Xk (k=1, 2, 3, 4) over cyclic group Zv (integers mod v) with parameters (v; k1, k2, k3, k4; λ) where X1 symmetric, X2=X3, and k1+2k2+k4=v+λ. also such (known families) parameter sets mentioned above excluding case when ki are equal. conjecture verified v≤53. Purpose: To construct to provide further support above-mentioned conjecture. Results: The first examples presented v=127 v=191. systematic computer search based on extended cover cases v=55, 57, 59, 61, 63. Practical relevance: used extensively in problems error-free coding, compression masking video information.